Proceedings of the International Conference on Cohomology of Arithmetic Groups, L-Functions, and Automorphic Forms

Proceedings of the International Conference on Cohomology of Arithmetic Groups, L-Functions, and Automorphic Forms PDF

Author: T. N. Venkataramana

Publisher: Alpha Science International, Limited

Published: 2001

Total Pages: 270

ISBN-13:

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This collection of papers is based on lectures delivered at the Tata Institute of Fundamental Research (TIFR) as part of a special year on arithmetic groups, $L$-functions and automorphic forms. The volume opens with an article by Cogdell and Piatetski-Shapiro on Converse Theorems for $GL_n$ and applications to liftings. It ends with some remarks on the Riemann Hypothesis by Ram Murty. Other talks cover topics such as Hecke theory for Jacobi forms, restriction maps and $L$-values, congruences for Hilbert modular forms, Whittaker models for $p$-adic $GL(4)$, the Seigel formula, newforms for the Maass Spezialchar, an algebraic Chebotarev density theorem, a converse theorem for Dirichlet series with poles, Kirillov theory for $GL_2(\mathcal{D})$, and the $L^2$ Euler characteristic of arithmetic quotients. The present volume is the latest in the Tata Institute's tradition of recognized contributions to number theory.

Cohomology of Arithmetic Groups and Automorphic Forms

Cohomology of Arithmetic Groups and Automorphic Forms PDF

Author: Jean-Pierre Labesse

Publisher: Springer

Published: 1990

Total Pages: 366

ISBN-13:

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Expansions of talks given at the conference held May 1989, Marseilles, France. Topics include modular symbols, Eisenstein series and cohomology, finiteness theorems for ball lattices, Hilbert modular forms, Lefschetz numbers for arithmetic groups. Annotation copyrighted by Book News, Inc., Portland, OR

Cohomology of Arithmetic Groups and Automorphic Forms

Cohomology of Arithmetic Groups and Automorphic Forms PDF

Author: Jean-Pierre Labesse

Publisher: Springer

Published: 2006-11-14

Total Pages: 358

ISBN-13: 3540468765

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Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.

L-Functions and Automorphic Forms

L-Functions and Automorphic Forms PDF

Author: Jan Hendrik Bruinier

Publisher: Springer

Published: 2018-02-22

Total Pages: 366

ISBN-13: 3319697129

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This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Computations with Modular Forms

Computations with Modular Forms PDF

Author: Gebhard Böckle

Publisher: Springer Science & Business Media

Published: 2014-01-23

Total Pages: 377

ISBN-13: 3319038478

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This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.