The Conference On L Functions

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The Conference on L-Functions

Lin Weng,Masanobu Kaneko
The Conference on L Functions Book PDF

Author : Lin Weng,Masanobu Kaneko
Publisher : World Scientific
Page : 383 pages
File Size : 42,9 Mb
Release : 2007
Category : Science
ISBN : 9789812705044

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The Conference on L-Functions by Lin Weng,Masanobu Kaneko Pdf

This invaluable volume collects papers written by many of the world's top experts on L-functions. It not only covers a wide range of topics from algebraic and analytic number theories, automorphic forms, to geometry and mathematical physics, but also treats the theory as a whole. The contributions reflect the latest, most advanced and most important aspects of L-functions. In particular, it contains Hida's lecture notes at the conference and at the Eigenvariety semester in Harvard University and Weng's detailed account of his works on high rank zeta functions and non-abelian L-functions.

L-Functions and Automorphic Forms

Jan Hendrik Bruinier,Winfried Kohnen
L Functions and Automorphic Forms Book PDF

Author : Jan Hendrik Bruinier,Winfried Kohnen
Publisher : Springer
Page : 366 pages
File Size : 45,7 Mb
Release : 2018-02-22
Category : Mathematics
ISBN : 9783319697123

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L-Functions and Automorphic Forms by Jan Hendrik Bruinier,Winfried Kohnen Pdf

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.

Arithmetic L-Functions and Differential Geometric Methods

Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot
Arithmetic L Functions and Differential Geometric Methods Book PDF

Author : Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot
Publisher : Springer Nature
Page : 324 pages
File Size : 50,7 Mb
Release : 2021-05-17
Category : Mathematics
ISBN : 9783030652036

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Arithmetic L-Functions and Differential Geometric Methods by Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot Pdf

This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: • Additive polylogarithms • Analytic torsions • Chabauty-Kim theory • Local Grothendieck-Riemann-Roch theorems • Periods • Syntomic regulator The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Automorphic Representations, L-Functions and Applications: Progress and Prospects

James W. Cogdell,Dihua Jiang,Stephen S. Kudla,David Soudry,Robert J. Stanton
Automorphic Representations L Functions and Applications Progress and Prospects Book PDF

Author : James W. Cogdell,Dihua Jiang,Stephen S. Kudla,David Soudry,Robert J. Stanton
Publisher : Walter de Gruyter
Page : 441 pages
File Size : 54,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110892703

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Automorphic Representations, L-Functions and Applications: Progress and Prospects by James W. Cogdell,Dihua Jiang,Stephen S. Kudla,David Soudry,Robert J. Stanton Pdf

This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.

Multiple Dirichlet Series, L-functions and Automorphic Forms

Daniel Bump,Solomon Friedberg,Dorian Goldfeld
Multiple Dirichlet Series L functions and Automorphic Forms Book PDF

Author : Daniel Bump,Solomon Friedberg,Dorian Goldfeld
Publisher : Springer
Page : 361 pages
File Size : 41,8 Mb
Release : 2012-07-09
Category : Mathematics
ISBN : 9780817683344

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Multiple Dirichlet Series, L-functions and Automorphic Forms by Daniel Bump,Solomon Friedberg,Dorian Goldfeld Pdf

Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

Arithmetic L-Functions and Differential Geometric Methods

Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot
Arithmetic L Functions and Differential Geometric Methods Book PDF

Author : Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot
Publisher : Birkhäuser
Page : 324 pages
File Size : 49,5 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 303065205X

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Arithmetic L-Functions and Differential Geometric Methods by Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot Pdf

This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: • Additive polylogarithms • Analytic torsions • Chabauty-Kim theory • Local Grothendieck-Riemann-Roch theorems • Periods • Syntomic regulator The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Beilinson's Conjectures on Special Values of L-Functions

M. Rapoport,P. Schneider,N. Schappacher
Beilinson s Conjectures on Special Values of L Functions Book PDF

Author : M. Rapoport,P. Schneider,N. Schappacher
Publisher : Academic Press
Page : 398 pages
File Size : 50,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483263304

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Beilinson's Conjectures on Special Values of L-Functions by M. Rapoport,P. Schneider,N. Schappacher Pdf

Beilinson's Conjectures on Special Values of L-Functions deals with Alexander Beilinson's conjectures on special values of L-functions. Topics covered range from Pierre Deligne's conjecture on critical values of L-functions to the Deligne-Beilinson cohomology, along with the Beilinson conjecture for algebraic number fields and Riemann-Roch theorem. Beilinson's regulators are also compared with those of Émile Borel. Comprised of 10 chapters, this volume begins with an introduction to the Beilinson conjectures and the theory of Chern classes from higher k-theory. The "simplest" example of an L-function is presented, the Riemann zeta function. The discussion then turns to Deligne's conjecture on critical values of L-functions and its connection to Beilinson's version. Subsequent chapters focus on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complex multiplication; and Beilinson's theorem on modular curves. The book concludes by reviewing the definition and properties of Deligne homology, as well as Hodge-D-conjecture. This monograph should be of considerable interest to researchers and graduate students who want to gain a better understanding of Beilinson's conjectures on special values of L-functions.

Advanced Analytic Number Theory: L-Functions

Carlos J. Moreno
Advanced Analytic Number Theory L Functions Book PDF

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 44,5 Mb
Release : 2005
Category : Algebraic number theory
ISBN : 9780821842669

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Advanced Analytic Number Theory: L-Functions by Carlos J. Moreno Pdf

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

Zeta and L -functions in Number Theory and Combinatorics

Wen-Ching Winnie Li
Zeta and L functions in Number Theory and Combinatorics Book PDF

Author : Wen-Ching Winnie Li
Publisher : American Mathematical Soc.
Page : 95 pages
File Size : 45,7 Mb
Release : 2019-03-01
Category : Combinatorial number theory
ISBN : 9781470449001

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Zeta and L -functions in Number Theory and Combinatorics by Wen-Ching Winnie Li Pdf

Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

On Certain $L$-Functions

James Arthur
On Certain L Functions Book PDF

Author : James Arthur
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 49,6 Mb
Release : 2011
Category : L-functions
ISBN : 9780821852040

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On Certain $L$-Functions by James Arthur Pdf

Illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their $L$-functions, and both local and global theory are addressed. Topics discussed in the articles include Langlands functoriality, the Rankin-Selberg method, the Langlands-Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of $p$-adic groups, Plancherel formula and its consequences, and the Gross-Prasad conjecture.

Value-Distribution of L-Functions

Jörn Steuding
Value Distribution of L Functions Book PDF

Author : Jörn Steuding
Publisher : Springer
Page : 322 pages
File Size : 48,7 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540448228

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Value-Distribution of L-Functions by Jörn Steuding Pdf

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.

Visions in Mathematics

Noga Alon,Jean Bourgain,Alain Connes,Misha Gromov,Vitali D. Milman
Visions in Mathematics Book PDF

Author : Noga Alon,Jean Bourgain,Alain Connes,Misha Gromov,Vitali D. Milman
Publisher : Birkhäuser
Page : 528 pages
File Size : 47,5 Mb
Release : 2010-04-14
Category : Mathematics
ISBN : 3034604246

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Visions in Mathematics by Noga Alon,Jean Bourgain,Alain Connes,Misha Gromov,Vitali D. Milman Pdf

"Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future.

The Theory of Zeta-Functions of Root Systems

Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura
The Theory of Zeta Functions of Root Systems Book PDF

Author : Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura
Publisher : Springer Nature
Page : 419 pages
File Size : 49,9 Mb
Release : 2024-02-03
Category : Mathematics
ISBN : 9789819909100

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The Theory of Zeta-Functions of Root Systems by Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura Pdf

The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.

Automorphic Forms, Representations and $L$-Functions

Armand Borel,W. Casselman,American Mathematical Society
Automorphic Forms Representations and L Functions Book PDF

Author : Armand Borel,W. Casselman,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 382 pages
File Size : 42,5 Mb
Release : 1979-06-30
Category : Mathematics
ISBN : 9780821814376

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Automorphic Forms, Representations and $L$-Functions by Armand Borel,W. Casselman,American Mathematical Society Pdf

Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions

Zeta Functions Of Reductive Groups And Their Zeros

Weng Lin
Zeta Functions Of Reductive Groups And Their Zeros Book PDF

Author : Weng Lin
Publisher : World Scientific
Page : 556 pages
File Size : 54,9 Mb
Release : 2018-02-07
Category : Mathematics
ISBN : 9789813230668

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Zeta Functions Of Reductive Groups And Their Zeros by Weng Lin Pdf

This book provides a systematic account of several breakthroughs in the modern theory of zeta functions. It contains two different approaches to introduce and study genuine zeta functions for reductive groups (and their maximal parabolic subgroups) defined over number fields. Namely, the geometric one, built up from stability of principal lattices and an arithmetic cohomology theory, and the analytic one, from Langlands' theory of Eisenstein systems and some techniques used in trace formula, respectively. Apparently different, they are unified via a Lafforgue type relation between Arthur's analytic truncations and parabolic reductions of Harder–Narasimhan and Atiyah–Bott. Dominated by the stability condition and/or the Lie structures embedded in, these zeta functions have a standard form of the functional equation, admit much more refined symmetric structures, and most surprisingly, satisfy a weak Riemann hypothesis. In addition, two levels of the distributions for their zeros are exposed, i.e. a classical one giving the Dirac symbol, and a secondary one conjecturally related to GUE. This book is written not only for experts, but for graduate students as well. For example, it offers a summary of basic theories on Eisenstein series and stability of lattices and arithmetic principal torsors. The second part on rank two zeta functions can be used as an introduction course, containing a Siegel type treatment of cusps and fundamental domains, and an elementary approach to the trace formula involved. Being in the junctions of several branches and advanced topics of mathematics, these works are very complicated, the results are fundamental, and the theory exposes a fertile area for further research. Contents: Non-Abelian Zeta Functions Rank Two Zeta Functions Eisenstein Periods and Multiple L-Functions Zeta Functions for Reductive Groups Algebraic, Analytic Structures and Rieman Hypothesis Geometric Structures and Riemann Hypothesis Five Essays on Arithmetic Cohomology Readership: Graduate students and researchers in the theory of zeta functions. Keywords: Zeta Function;Riemann Hypothesis;Stability;Lattice;Fundamental Domain;Reductive Group;Root System;Eisenstein Series;Truncation;Arithmetic Principal Torsor;Adelic CohomologyReview: Key Features: Genuine zeta functions for reductive groups over number fields are introduced and studied systematically, based on (i) fine parabolic structures and Lie structures involved, (ii) a new stability theory for arithmetic principal torsors over number fields, and (iii) trace formula via a geometric understanding of Arthur's analytic truncations For the first time in history, we prove a weak Riemann hypothesis for zeta functions of reductive groups defined over number fields Not only the theory is explained, but the process of building the theory is elaborated in great detail