Analytic Methods in Arithmetic Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 1470437848
Total Pages : 248 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Analytic Methods in Arithmetic Geometry by : Alina Bucur

Download or read book Analytic Methods in Arithmetic Geometry written by Alina Bucur and published by American Mathematical Soc.. This book was released on 2019-11-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with SL2(Fq) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from ℓ-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.

Analytic Methods in Algebraic Geometry

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Publisher :
ISBN 13 : 9787040305319
Total Pages : 231 pages
Book Rating : 4.3/5 (53 download)

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Book Synopsis Analytic Methods in Algebraic Geometry by : Jean-Pierre Demailly

Download or read book Analytic Methods in Algebraic Geometry written by Jean-Pierre Demailly and published by . This book was released on 2010 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetic Geometry and Number Theory

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Publisher : World Scientific
ISBN 13 : 981256814X
Total Pages : 414 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Arithmetic Geometry and Number Theory by : Lin Weng

Download or read book Arithmetic Geometry and Number Theory written by Lin Weng and published by World Scientific. This book was released on 2006 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.

Higher Geometry

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Publisher :
ISBN 13 :
Total Pages : 435 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis Higher Geometry by : Frederick Shenstone Woods

Download or read book Higher Geometry written by Frederick Shenstone Woods and published by . This book was released on 1922 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Developments and Retrospectives in Lie Theory

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Publisher : Springer
ISBN 13 : 3319099345
Total Pages : 274 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Developments and Retrospectives in Lie Theory by : Geoffrey Mason

Download or read book Developments and Retrospectives in Lie Theory written by Geoffrey Mason and published by Springer. This book was released on 2014-11-12 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. At the beginning, the top universities in California and Utah hosted the meetings, which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. These Lie theory workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. The contributors have all participated in these Lie theory workshops and include in this volume expository articles which will cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Analytic and Algebraic Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821849088
Total Pages : 583 pages
Book Rating : 4.8/5 (49 download)

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Book Synopsis Analytic and Algebraic Geometry by : Jeffery D. McNeal

Download or read book Analytic and Algebraic Geometry written by Jeffery D. McNeal and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the 'other side' of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists."--Publisher's description.

History of Analytic Geometry

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Publisher : Courier Corporation
ISBN 13 : 0486154513
Total Pages : 306 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis History of Analytic Geometry by : Carl B. Boyer

Download or read book History of Analytic Geometry written by Carl B. Boyer and published by Courier Corporation. This book was released on 2012-06-28 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study presents the concepts and contributions from before the Alexandrian Age through to Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. 1956 edition. Analytical bibliography. Index.

Arithmetic Geometry, Number Theory, and Computation

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Publisher : Springer Nature
ISBN 13 : 3030809145
Total Pages : 587 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Arithmetic Geometry, Number Theory, and Computation by : Jennifer S. Balakrishnan

Download or read book Arithmetic Geometry, Number Theory, and Computation written by Jennifer S. Balakrishnan and published by Springer Nature. This book was released on 2022-03-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.

Capacity Theory with Local Rationality

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Publisher : American Mathematical Soc.
ISBN 13 : 1470409801
Total Pages : 466 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Capacity Theory with Local Rationality by : Robert Rumely

Download or read book Capacity Theory with Local Rationality written by Robert Rumely and published by American Mathematical Soc.. This book was released on 2013-12-26 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities. Another chapter contains extensions of the theorem, including variants on Berkovich curves. The proof uses both algebraic and analytic methods, and draws on arithmetic and algebraic geometry, potential theory, and approximation theory. It introduces new ideas and tools which may be useful in other settings, including the local action of the Jacobian on a curve, the "universal function" of given degree on a curve, the theory of inner capacities and Green's functions, and the construction of near-extremal approximating functions by means of the canonical distance.

Higher Geometry

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Publisher : Forgotten Books
ISBN 13 : 9781330071908
Total Pages : 437 pages
Book Rating : 4.0/5 (719 download)

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Book Synopsis Higher Geometry by : Frederick S. Woods

Download or read book Higher Geometry written by Frederick S. Woods and published by Forgotten Books. This book was released on 2015-06-14 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry The present book is the outgrowth of lectures given at various times to students of the later undergraduate and earlier graduate years. It aims to present some of the general concepts and methods which are necessary for advanced work in algebraic geometry (as distinguished from differential geometry), but which are not now accessible to the student in any one volume, and thus to bridge the gap between the. usual text in analytic geometry and treatises or articles on special topics. With this object in view the author has assumed very little mathematical preparation on the part of the student beyond that acquired in elementary courses in calculus and plane analytic geometry. In addition it has been necessary to assume a slight knowledge of determinants, especially as applied to the solution of linear equations, such as may be acquired in a very short course on the subject. But it has not been assumed that the student has had a course in higher algebra, including matrices, linear substitutions, invariants, and similar topics, and no effort has been made to include a discussion of these subjects in the text. This restriction in the tools to be used necessitates at times modes of expression and methods of proof which are a little cumbersome, but the appeal to a larger number of readers seems to justify the occasional lack of elegance. In preparing the text one of the greatest problems has consisted in determining what matters to exclude. It is-obvious that an introduction to geometry cannot contain all that is known on any subject or even refer briefly to all general topics. The matter of selection is necessarily one of individual judgment. One large domain of geometry has been definitely excluded from the plan of the book; namely, that of differential geometry. In the field which is left the author cannot dare to hope that his choice of material will agree exactly with that which would be made by any other teacher. He hopes, however, that his choice has been sufficiently wise to make the book useful to many besides himself. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Analytic Topology

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Publisher :
ISBN 13 : 9781258234164
Total Pages : 292 pages
Book Rating : 4.2/5 (341 download)

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Book Synopsis Analytic Topology by : Gordon Thomas Whyburn

Download or read book Analytic Topology written by Gordon Thomas Whyburn and published by . This book was released on 2012-03-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Women in Numbers Europe II

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Publisher : Springer
ISBN 13 : 3319749986
Total Pages : 218 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Women in Numbers Europe II by : Irene I. Bouw

Download or read book Women in Numbers Europe II written by Irene I. Bouw and published by Springer. This book was released on 2018-06-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work.

Modular Forms and Fermat’s Last Theorem

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Publisher : Springer Science & Business Media
ISBN 13 : 1461219744
Total Pages : 592 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Modular Forms and Fermat’s Last Theorem by : Gary Cornell

Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

Number Theory and Algebraic Geometry

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Publisher : Cambridge University Press
ISBN 13 : 9780521545181
Total Pages : 312 pages
Book Rating : 4.5/5 (451 download)

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Book Synopsis Number Theory and Algebraic Geometry by : Miles Reid

Download or read book Number Theory and Algebraic Geometry written by Miles Reid and published by Cambridge University Press. This book was released on 2003 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

Introduction to Analytic Geometry

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Publisher : Forgotten Books
ISBN 13 : 9781330868195
Total Pages : 236 pages
Book Rating : 4.8/5 (681 download)

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Book Synopsis Introduction to Analytic Geometry by : Percey Franklyn Smith

Download or read book Introduction to Analytic Geometry written by Percey Franklyn Smith and published by Forgotten Books. This book was released on 2015-06-04 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Introduction to Analytic Geometry In preparing this volume the authors have endeavored to write a drill book for beginners which presents, in a manner conforming with modern ideas, the fundamental concepts of the subject. The subject-matter is slightly more than the minimum required for the calculus, but only as much more as is necessary to permit of some choice on the part of the teacher. It is believed that the text is complete for students finishing their study of mathematics with a course in Analytic Geometry. The authors have intentionally avoided giving the book the form of a treatise on conic sections. Conic sections naturally appear, but chiefly as illustrative of general analytic methods. Attention is called to the method of treatment. The subject is developed after the Euclidean method of definition and theorem, without, however, adhering to formal presentation. The advantage is obvious, for the student is made sure of the exact nature of each acquisition. Again, each method is summarized in a rule stated in consecutive steps. This is a gain in clearness. Many illustrative examples are worked out in the text. Emphasis has everywhere been put upon the analytic side, that is, the student is taught to start from the equation. He is shown how to work with the figure as a guide, but is warned not to use it in any other way. Chapter III may be referred to in this connection. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Geometric Methods in Algebra and Number Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 0817644172
Total Pages : 365 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometric Methods in Algebra and Number Theory by : Fedor Bogomolov

Download or read book Geometric Methods in Algebra and Number Theory written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

Higher Geometry

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Publisher :
ISBN 13 :
Total Pages : 433 pages
Book Rating : 4.:/5 (819 download)

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Book Synopsis Higher Geometry by : Frederic S. Woods

Download or read book Higher Geometry written by Frederic S. Woods and published by . This book was released on 1961 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: