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Author : Werner Hoffmann
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Trace Formula for Hecke Operators Over Rank One Lattices written by Werner Hoffmann and published by . This book was released on 1986 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Werner Müller
Publisher : Springer
ISBN 13 : 3319948334
Total Pages : 461 pages
Book Rating : 4.3/5 (199 download)
Download or read book Geometric Aspects of the Trace Formula written by Werner Müller and published by Springer. This book was released on 2018-10-11 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.
Author : Bert-Wolfgang Schulze
Publisher :
ISBN 13 :
Total Pages : 340 pages
Book Rating : 4.:/5 (25 download)
Download or read book Seminar Analysis of the Karl-Weierstrass- Institute of Mathematics, Academy of Sciences of the GDR, 1986/87 written by Bert-Wolfgang Schulze and published by . This book was released on 1988 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Audrey Terras
Publisher : Springer
ISBN 13 : 1493934082
Total Pages : 500 pages
Book Rating : 4.4/5 (939 download)
Download or read book Harmonic Analysis on Symmetric Spaces—Higher Rank Spaces, Positive Definite Matrix Space and Generalizations written by Audrey Terras and published by Springer. This book was released on 2016-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations. It is intended for beginning graduate students in mathematics or researchers in physics or engineering. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples, history, and applications. The symmetric spaces considered here are quotients X=G/K, where G is a non-compact real Lie group, such as the general linear group GL(n,P) of all n x n non-singular real matrices, and K=O(n), the maximal compact subgroup of orthogonal matrices. Other examples are Siegel's upper half "plane" and the quaternionic upper half "plane". In the case of the general linear group, one can identify X with the space Pn of n x n positive definite symmetric matrices. Many corrections and updates have been incorporated in this new edition. Updates include discussions of random matrix theory and quantum chaos, as well as recent research on modular forms and their corresponding L-functions in higher rank. Many applications have been added, such as the solution of the heat equation on Pn, the central limit theorem of Donald St. P. Richards for Pn, results on densest lattice packing of spheres in Euclidean space, and GL(n)-analogs of the Weyl law for eigenvalues of the Laplacian in plane domains. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, fundamental domains in X for discrete groups Γ (such as the modular group GL(n,Z) of n x n matrices with integer entries and determinant ±1), connections with the problem of finding densest lattice packings of spheres in Euclidean space, automorphic forms, Hecke operators, L-functions, and the Selberg trace formula and its applications in spectral theory as well as number theory.
Author :
Publisher :
ISBN 13 :
Total Pages : 1100 pages
Book Rating : 4.X/5 (6 download)
Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 1100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dorian Goldfeld
Publisher : Springer Science & Business Media
ISBN 13 : 1461412595
Total Pages : 715 pages
Book Rating : 4.4/5 (614 download)
Download or read book Number Theory, Analysis and Geometry written by Dorian Goldfeld and published by Springer Science & Business Media. This book was released on 2011-12-20 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of Serge Lang’s vast contribution to mathematics, this memorial volume presents articles by prominent mathematicians. Reflecting the breadth of Lang's own interests and accomplishments, these essays span the field of Number Theory, Analysis and Geometry.
Author :
Publisher :
ISBN 13 :
Total Pages : 1032 pages
Book Rating : 4.:/5 (51 download)
Download or read book Reviews in Number Theory, 1984-96 written by and published by . This book was released on 1997 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)
Download or read book Seminar Analysis of the Karl-Weierstrass-Institute of Mathematics written by and published by . This book was released on 1986 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin Eichler
Publisher : Springer Science & Business Media
ISBN 13 : 1468491628
Total Pages : 156 pages
Book Rating : 4.4/5 (684 download)
Download or read book The Theory of Jacobi Forms written by Martin Eichler and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.
Author : Werner Müller
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.3/5 (91 download)
Download or read book Spectral Theory for Riemannian Manifolds with Cusps and a Related Trace Formula written by Werner Müller and published by . This book was released on 1982 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gaëtan Chenevier
Publisher : Springer
ISBN 13 : 3319958917
Total Pages : 428 pages
Book Rating : 4.3/5 (199 download)
Download or read book Automorphic Forms and Even Unimodular Lattices written by Gaëtan Chenevier and published by Springer. This book was released on 2019-02-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Myung-Hwan Kim
Publisher : American Mathematical Soc.
ISBN 13 : 0821819496
Total Pages : 314 pages
Book Rating : 4.8/5 (218 download)
Download or read book Integral Quadratic Forms and Lattices written by Myung-Hwan Kim and published by American Mathematical Soc.. This book was released on 1999 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more. Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.
Author : Gian-Carlo Rota
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.:/5 (49 download)
Download or read book Studies in Algebra and Number Theory written by Gian-Carlo Rota and published by . This book was released on 1979 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Herb
Publisher : Springer
ISBN 13 : 3540389369
Total Pages : 465 pages
Book Rating : 4.5/5 (43 download)
Download or read book Lie Group Representations III written by R. Herb and published by Springer. This book was released on 2006-11-14 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A.B. Venkov
Publisher : Springer Science & Business Media
ISBN 13 : 9400918925
Total Pages : 189 pages
Book Rating : 4.4/5 (9 download)
Download or read book Spectral Theory of Automorphic Functions written by A.B. Venkov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait su comment en revcnrr, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back. Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838440
Total Pages : 708 pages
Book Rating : 4.8/5 (384 download)
Download or read book Harmonic Analysis, the Trace Formula, and Shimura Varieties written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2005 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
Author : Kathrin Bringmann
Publisher : American Mathematical Soc.
ISBN 13 : 1470419440
Total Pages : 409 pages
Book Rating : 4.4/5 (74 download)
Download or read book Harmonic Maass Forms and Mock Modular Forms: Theory and Applications written by Kathrin Bringmann and published by American Mathematical Soc.. This book was released on 2017-12-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.
