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Automorphic Forms And Related Topics
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Book Synopsis Topics in Classical Automorphic Forms by : Henryk Iwaniec
Download or read book Topics in Classical Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Soc.. This book was released on 1997 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Modular Forms and Related Topics in Number Theory by : B. Ramakrishnan
Download or read book Modular Forms and Related Topics in Number Theory written by B. Ramakrishnan and published by Springer Nature. This book was released on 2020-11-24 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the papers presented at the Conference on Number Theory, held at the Kerala School of Mathematics, Kozhikode, Kerala, India, from December 10–14, 2018. The conference aimed at bringing the active number theorists and researchers in automorphic forms and allied areas to demonstrate their current research works. This book benefits young research scholars, postdoctoral fellows, and young faculty members working in these areas of research.
Book Synopsis Automorphic Forms on GL (3,TR) by : D. Bump
Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Methods of Automorphic Forms by : Henryk Iwaniec
Download or read book Spectral Methods of Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain. This book was released on 2021-11-17 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
Book Synopsis Automorphic Forms by : Anton Deitmar
Download or read book Automorphic Forms written by Anton Deitmar and published by Springer Science & Business Media. This book was released on 2012-08-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Book Synopsis Automorphic Forms and Related Topics by : Samuele Anni
Download or read book Automorphic Forms and Related Topics written by Samuele Anni and published by American Mathematical Soc.. This book was released on 2019-06-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.
Book Synopsis Families of Automorphic Forms and the Trace Formula by : Werner Müller
Download or read book Families of Automorphic Forms and the Trace Formula written by Werner Müller and published by Springer. This book was released on 2016-09-20 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.
Book Synopsis Some Applications of Modular Forms by : Peter Sarnak
Download or read book Some Applications of Modular Forms written by Peter Sarnak and published by Cambridge University Press. This book was released on 1990-11-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics and computer science.
Book Synopsis Automorphic Forms and Applications by : Peter Sarnak
Download or read book Automorphic Forms and Applications written by Peter Sarnak and published by American Mathematical Soc.. This book was released on 2007 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field. The book starts with the lectures of Borel on the basic theory of automorphic forms, which lay the foundation for the lectures by Cogdell and Shahidi on converse theorems and the Langlands-Shahidi method, as well as those by Clozel and Li on the Ramanujan conjectures and graphs. The analytic theory of GL(2)-forms and $L$-functions are the subject of Michel's lectures, while Terras covers arithmetic quantum chaos. The volume also includes a chapter by Vogan on isolated unitary representations, which is related to the lectures by Clozel. This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory. the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Book Synopsis Automorphic Forms and L-Functions for the Group GL(n,R) by : Dorian Goldfeld
Download or read book Automorphic Forms and L-Functions for the Group GL(n,R) written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2006-08-03 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Book Synopsis Automorphic Forms on GL (2) by : H. Jacquet
Download or read book Automorphic Forms on GL (2) written by H. Jacquet and published by Springer. This book was released on 2006-11-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representation Theory and Automorphic Forms by : Toshiyuki Kobayashi
Download or read book Representation Theory and Automorphic Forms written by Toshiyuki Kobayashi and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.
Book Synopsis Automorphic Forms on Adele Groups. (AM-83), Volume 83 by : Stephen S. Gelbart
Download or read book Automorphic Forms on Adele Groups. (AM-83), Volume 83 written by Stephen S. Gelbart and published by Princeton University Press. This book was released on 2016-03-02 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?
Book Synopsis Conformal Field Theory, Automorphic Forms and Related Topics by : Winfried Kohnen
Download or read book Conformal Field Theory, Automorphic Forms and Related Topics written by Winfried Kohnen and published by Springer. This book was released on 2014-08-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).
Book Synopsis Introductory Lectures on Automorphic Forms by : Walter L. Baily Jr.
Download or read book Introductory Lectures on Automorphic Forms written by Walter L. Baily Jr. and published by Princeton University Press. This book was released on 2015-03-08 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn). Part I, essentially elementary, deals with complex analytic automorphic forms on a bounded domain; it presents H. Cartan's proof of the existence of the projective imbedding of the compact quotient of such a domain by a discrete group. Part II treats the construction and properties of automorphic forms with respect to an arithmetic group acting on a bounded symmetric domain; this part is highly technical, and based largely on relevant results in functional analysis due to Godement and Harish-Chandra. In Part III, Professor Baily extends the discussion to include some special topics, specifically, the arithmetic propertics of Eisenstein series and their connection with the arithmetic theory of quadratic forms. Unlike classical works on the subject, this book deals with more than one variable, and it differs notably in its treatment of analysis on the group of automorphisms of the domain. It is concerned with the case of complex analytic automorphic forms because of their connection with algebraic geometry, and so is distinct from other modern treatises that deal with automorphic forms on a semi-simple Lie group. Having had its inception as graduate- level lectures, the book assumes some knowledge of complex function theory and algebra, for the serious reader is expected to supply certain details for himself, especially in such related areas as functional analysis and algebraic groups. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Introduction to the Arithmetic Theory of Automorphic Functions by : Gorō Shimura
Download or read book Introduction to the Arithmetic Theory of Automorphic Functions written by Gorō Shimura and published by Princeton University Press. This book was released on 1971-08-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Book Synopsis Automorphic Forms, Representations and $L$-Functions by : Armand Borel
Download or read book Automorphic Forms, Representations and $L$-Functions written by Armand Borel and published by American Mathematical Soc.. This book was released on 1979-06-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
