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| Author | : Anton Deitmar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 255 |
| Release | : 2012-08-29 |
| Genre | : Mathematics |
| ISBN | : 144714435X |
Download Automorphic Forms Book in PDF, ePub and Kindle
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.
| Author | : Henryk Iwaniec |
| Publisher | : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain |
| Total Pages | : 220 |
| Release | : 2021-11-17 |
| Genre | : Mathematics |
| ISBN | : 1470466228 |
Download Spectral Methods of Automorphic Forms Book in PDF, ePub and Kindle
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.
| Author | : D. Bump |
| Publisher | : Springer |
| Total Pages | : 196 |
| Release | : 2006-12-08 |
| Genre | : Mathematics |
| ISBN | : 3540390553 |
Download Automorphic Forms on GL (3,TR) Book in PDF, ePub and Kindle
| Author | : Henryk Iwaniec |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 274 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821807773 |
Download Topics in Classical Automorphic Forms Book in PDF, ePub and Kindle
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
| Author | : H. Jacquet |
| Publisher | : Springer |
| Total Pages | : 156 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540376127 |
Download Automorphic Forms on GL (2) Book in PDF, ePub and Kindle
| Author | : Toshiyuki Kobayashi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 220 |
| Release | : 2007-10-10 |
| Genre | : Mathematics |
| ISBN | : 0817646469 |
Download Representation Theory and Automorphic Forms Book in PDF, ePub and Kindle
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.
| Author | : Gaëtan Chenevier |
| Publisher | : Springer |
| Total Pages | : 417 |
| Release | : 2019-02-28 |
| Genre | : Mathematics |
| ISBN | : 3319958917 |
Download Automorphic Forms and Even Unimodular Lattices Book in PDF, ePub and Kindle
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
| Author | : Dorian Goldfeld |
| Publisher | : Cambridge University Press |
| Total Pages | : 65 |
| Release | : 2006-08-03 |
| Genre | : Mathematics |
| ISBN | : 1139456202 |
Download Automorphic Forms and L-Functions for the Group GL(n,R) Book in PDF, ePub and Kindle
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.
| Author | : A. Weil |
| Publisher | : Springer |
| Total Pages | : 170 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540365028 |
Download Dirichlet Series and Automorphic Forms Book in PDF, ePub and Kindle
| Author | : Werner Müller |
| Publisher | : Springer |
| Total Pages | : 581 |
| Release | : 2016-09-20 |
| Genre | : Mathematics |
| ISBN | : 3319414240 |
Download Families of Automorphic Forms and the Trace Formula Book in PDF, ePub and Kindle
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.
