Quaternion Orders, Quadratic Forms, and Shimura Curves

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821833599
Total Pages : 232 pages
Book Rating : 4.8/5 (335 download)

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Book Synopsis Quaternion Orders, Quadratic Forms, and Shimura Curves by : Montserrat Alsina

Download or read book Quaternion Orders, Quadratic Forms, and Shimura Curves written by Montserrat Alsina and published by American Mathematical Soc.. This book was released on 2004 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. This monograph presents Shimura curves from a theoretical and algorithmic perspective. The main topics are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplicationpoints. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities that parallels Gauss'theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. This is one of the few available books explaining the theory of Shimura curves at the graduate student level. Each topic covered in the book begins with a theoretical discussion followed by carefully worked-out examples, preparing the way for further research.

Quaternion Orders, Quadratic Forms, and Shimura Curves

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821869833
Total Pages : 216 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quaternion Orders, Quadratic Forms, and Shimura Curves by : Montserrat Alsina and Pilar Bayer

Download or read book Quaternion Orders, Quadratic Forms, and Shimura Curves written by Montserrat Alsina and Pilar Bayer and published by American Mathematical Soc.. This book was released on with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. This monograph presents Shimura curves from a theoretical and algorithmic perspective. The main topics are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities that parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. This is one of the few available books explaining the theory of Shimura curves at the graduate student level. Each topic covered in the book begins with a theoretical discussion followed by carefully worked-out examples, preparing the way for further research. Titles in this series are co-published with the Centre de Recherches Mathématiques.

Selecta Pilar Bayer. Volum II

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Publisher : Edicions Universitat Barcelona
ISBN 13 : 8447539571
Total Pages : 372 pages
Book Rating : 4.4/5 (475 download)

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Book Synopsis Selecta Pilar Bayer. Volum II by : Montserrat Alsina

Download or read book Selecta Pilar Bayer. Volum II written by Montserrat Alsina and published by Edicions Universitat Barcelona. This book was released on 2016-01-20 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: L’obra incomparable de Pilar Bayer està escrita en les persones,en totes les persones a les quals, en un moment o altre, ens ha fet gaudir del plaer d’escoltar matemàtiques, d’aprendre matemàtiques, de fer matemàtiques. Aquesta obra diversa, eclèctica, rica en mil matisos, roman en el terreny de les experiències personals que fan la nostra vida més interessant, i no la podem plasmar en un volum, ni en dos. És un llegat fantàstic que portem incorporat. Els treballs recopilats en aquests volums en ocasió del setantè aniversari de Pilar Bayer mostren en un format palpable l’amplitud de la seva òptica matemàtica, la profunditat i la bellesa de les seves matemàtiques. No és un recull exhaustiu, sinó una invitació perquè el lector faci un tastet d’allò que li agradi més. Després, ja no podrà parar. La persona i l’obra el captivaran per seguir endavant.

Algorithmic Number Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 3540360751
Total Pages : 609 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Algorithmic Number Theory by : Florian Hess

Download or read book Algorithmic Number Theory written by Florian Hess and published by Springer Science & Business Media. This book was released on 2006-07-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, Germany in July 2006. The 37 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.

Arithmetic Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 0821844768
Total Pages : 570 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Arithmetic Geometry by : Clay Mathematics Institute. Summer School

Download or read book Arithmetic Geometry written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2009 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.

Women in Numbers Europe III

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Publisher : Springer Nature
ISBN 13 : 3030777006
Total Pages : 334 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Women in Numbers Europe III by : Alina Carmen Cojocaru

Download or read book Women in Numbers Europe III written by Alina Carmen Cojocaru and published by Springer Nature. This book was released on 2022-02-01 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of collaborations started at the 3rd edition of the Women in Numbers Europe (WINE) conference between senior and mid-level faculty, junior faculty, postdocs, and graduate students. The contents of this book should be of interest to graduate students and researchers in number theory.

Models and Theories in Social Systems

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Publisher : Springer
ISBN 13 : 3030000842
Total Pages : 576 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Models and Theories in Social Systems by : Cristina Flaut

Download or read book Models and Theories in Social Systems written by Cristina Flaut and published by Springer. This book was released on 2018-10-12 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concisely presents a broad range of models and theories on social systems. Because of the huge spectrum of topics involving social systems, various issues related to Mathematics, Statistics, Teaching, Social Science, and Economics are discussed. In an effort to introduce the subject to a wider audience, this volume, part of the series “Studies in Systems, Decision and Control”, equally addresses the needs of mathematicians, statisticians, sociologists and philosophers. The studies examined here are divided into four parts. The first part, “Perusing the Minds Behind Scientific Discoveries”, traces the winding path of Syamal K. Sen and Ravi P. Agarwal’s scholarship throughout history, and most importantly, the thought processes that allowed each of them to master their subject. The second part covers “Theories in Social Systems” and the third discusses “Models in Social Systems”, while the fourth and final part is dedicated to “Mathematical Methods in the Social Sciences”. Given its breadth of coverage, the book will offer inquisitive readers a valuable point of departure for exploring these rich, vast, and ever-expanding fields of knowledge.

WIN -- Women in Numbers

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Publisher : American Mathematical Soc.
ISBN 13 : 0821852264
Total Pages : 300 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis WIN -- Women in Numbers by : Alina Carmen Cojocaru

Download or read book WIN -- Women in Numbers written by Alina Carmen Cojocaru and published by American Mathematical Soc.. This book was released on 2011 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of papers on number theory which evolved out of the workshop WIN-Women In Numbers, held November 2-7, 2008. It includes articles showcasing outcomes from collaborative research initiated during the workshop as well as survey papers aimed at introducing graduate students and recent PhDs to important research topics in number theory.

Computational Methods for Three-Dimensional Microscopy Reconstruction

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Publisher : Springer Science & Business Media
ISBN 13 : 1461495210
Total Pages : 275 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Computational Methods for Three-Dimensional Microscopy Reconstruction by : Gabor T. Herman

Download or read book Computational Methods for Three-Dimensional Microscopy Reconstruction written by Gabor T. Herman and published by Springer Science & Business Media. This book was released on 2014-01-29 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approaches to the recovery of three-dimensional information on a biological object, which are often formulated or implemented initially in an intuitive way, are concisely described here based on physical models of the object and the image-formation process. Both three-dimensional electron microscopy and X-ray tomography can be captured in the same mathematical framework, leading to closely-related computational approaches, but the methodologies differ in detail and hence pose different challenges. The editors of this volume, Gabor T. Herman and Joachim Frank, are experts in the respective methodologies and present research at the forefront of biological imaging and structural biology. Computational Methods for Three-Dimensional Microscopy Reconstruction will serve as a useful resource for scholars interested in the development of computational methods for structural biology and cell biology, particularly in the area of 3D imaging and modeling.

Modular Forms and Special Cycles on Shimura Curves. (AM-161)

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Publisher : Princeton University Press
ISBN 13 : 1400837162
Total Pages : 384 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Modular Forms and Special Cycles on Shimura Curves. (AM-161) by : Stephen S. Kudla

Download or read book Modular Forms and Special Cycles on Shimura Curves. (AM-161) written by Stephen S. Kudla and published by Princeton University Press. This book was released on 2006-04-04 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" attached to a Shimura curve "M" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of "M". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.

Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures

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Publisher : American Mathematical Soc.
ISBN 13 : 1470419475
Total Pages : 238 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures by : David Kohel

Download or read book Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures written by David Kohel and published by American Mathematical Soc.. This book was released on 2016-04-26 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Winter School and Workshop on Frobenius Distributions on Curves, held from February 17–21, 2014 and February 24–28, 2014, at the Centre International de Rencontres Mathématiques, Marseille, France. This volume gives a representative sample of current research and developments in the rapidly developing areas of Frobenius distributions. This is mostly driven by two famous conjectures: the Sato-Tate conjecture, which has been recently proved for elliptic curves by L. Clozel, M. Harris and R. Taylor, and the Lang-Trotter conjecture, which is still widely open. Investigations in this area are based on a fine mix of algebraic, analytic and computational techniques, and the papers contained in this volume give a balanced picture of these approaches.

Locally Mixed Symmetric Spaces

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Publisher : Springer Nature
ISBN 13 : 3030698041
Total Pages : 622 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Locally Mixed Symmetric Spaces by : Bruce Hunt

Download or read book Locally Mixed Symmetric Spaces written by Bruce Hunt and published by Springer Nature. This book was released on 2021-09-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.

Quadratic Forms and Quaternion Algebras

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Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis Quadratic Forms and Quaternion Algebras by : John Michael Voight

Download or read book Quadratic Forms and Quaternion Algebras written by John Michael Voight and published by . This book was released on 2005 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quaternion Algebras

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Publisher : Springer Nature
ISBN 13 : 3030566943
Total Pages : 877 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Quaternion Algebras by : John Voight

Download or read book Quaternion Algebras written by John Voight and published by Springer Nature. This book was released on 2021-06-28 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 940 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Variations on a Theme of Euler

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Publisher : Springer Science & Business Media
ISBN 13 : 1475723261
Total Pages : 356 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Variations on a Theme of Euler by : Takashi Ono

Download or read book Variations on a Theme of Euler written by Takashi Ono and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first six chapters and Appendix 1 of this book appeared in Japanese in a book of the same title 15years aga (Jikkyo, Tokyo, 1980).At the request of some people who do not wish to learn Japanese, I decided to rewrite my old work in English. This time, I added a chapter on the arithmetic of quadratic maps (Chapter 7) and Appendix 2, A Short Survey of Subsequent Research on Congruent Numbers, by M. Kida. Some 20 years ago, while rifling through the pages of Selecta Heinz Hopj (Springer, 1964), I noticed a system of three quadratic forms in four variables with coefficientsin Z that yields the map of the 3-sphere to the 2-sphere with the Hopf invariant r =1 (cf. Selecta, p. 52). Immediately I feit that one aspect of classical and modern number theory, including quadratic forms (Pythagoras, Fermat, Euler, and Gauss) and space elliptic curves as intersection of quadratic surfaces (Fibonacci, Fermat, and Euler), could be considered as the number theory of quadratic maps-especially of those maps sending the n-sphere to the m-sphere, i.e., the generalized Hopf maps. Having these in mind, I deliveredseverallectures at The Johns Hopkins University (Topics in Number Theory, 1973-1974, 1975-1976, 1978-1979, and 1979-1980). These lectures necessarily contained the following three basic areas of mathematics: v vi Preface Theta Simple Functions Aigebras Elliptic Curves Number Theory Figure P.l.

Periods of Quaternionic Shimura Varieties

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Publisher :
ISBN 13 : 9781470464189
Total Pages : pages
Book Rating : 4.4/5 (641 download)

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Book Synopsis Periods of Quaternionic Shimura Varieties by : Atsushi Ichino

Download or read book Periods of Quaternionic Shimura Varieties written by Atsushi Ichino and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of L-functions and constructing geometric realizations of Lan.