The Conference On L Functions

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The Conference on L-Functions

Author : Lin Weng
Publisher : World Scientific
ISBN 13 : 9812772391
Total Pages : 383 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis The Conference on L-Functions by : Lin Weng

Download or read book The Conference on L-Functions written by Lin Weng and published by World Scientific. This book was released on 2007 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Sample Chapter(s). Chapter 1: Quantum Maass Forms (435 KB). Contents: Quantum Maass Forms (R Bruggeman); o-invariant of p -Adic L -Functions (H Hida); Siegel Modular Forms of Weight Three and Conjectural Correspondence of Shimura Type and Langlands Type (T Ibukiyama); Convolutions of Fourier Coefficients of Cusp Forms and the Circle Method (M Jutila); On an Extension of the Derivation Relation for Multiple Zeta Values (M Kaneko); On Symmetric Powers of Cusp Forms on GL 2 (H H Kim); Zeta Functions of Root Systems (Y Komori et al.); Sums of Kloosterman Sums Revisted (Y Motohashi); The LindelAf Class of L -Functions (K Murty); A Proof of the Riemann Hypothesis for the Weng Zeta Function of Rank 3 for the Rationals (M Suzuki); Elliptic Curves Arising from the Spectral Zeta Function for Non-Commutative Harmonic Oscillators and o 0 (4)-Modular Forms (K Kimoto & M Wakayama); A Geometric Approach to L -Functions (L Weng). Readership: Graduate students, lecturers, and active researchers in various branches of mathematics, such as algebra, analysis, geometry and mathematical physics."

The Conference on L-Functions

Author : Lin Weng
Publisher : World Scientific
ISBN 13 : 981270504X
Total Pages : 383 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis The Conference on L-Functions by : Lin Weng

On Certain $L$-Functions

Author : James Arthur
Publisher : American Mathematical Soc.
ISBN 13 : 0821852043
Total Pages : 658 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Certain $L$-Functions by : James Arthur

Download or read book On Certain $L$-Functions written by James Arthur and published by American Mathematical Soc.. This book was released on 2011 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

L-Functions and Automorphic Forms

Author : Jan Hendrik Bruinier
Publisher : Springer
ISBN 13 : 3319697129
Total Pages : 367 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis L-Functions and Automorphic Forms by : Jan Hendrik Bruinier

Download or read book L-Functions and Automorphic Forms written by Jan Hendrik Bruinier and published by Springer. This book was released on 2018-02-22 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advanced Analytic Number Theory: L-Functions

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
ISBN 13 : 0821842668
Total Pages : 313 pages
Book Rating : 4.8/5 (218 download)

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

Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno and published by American Mathematical Soc.. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Beilinson's Conjectures on Special Values of L-Functions

Author : M. Rapoport
Publisher : Academic Press
ISBN 13 : 1483263304
Total Pages : 399 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Beilinson's Conjectures on Special Values of L-Functions by : M. Rapoport

Download or read book Beilinson's Conjectures on Special Values of L-Functions written by M. Rapoport and published by Academic Press. This book was released on 2014-07-14 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Zeta and L -functions in Number Theory and Combinatorics

Author : Wen-Ching Winnie Li
Publisher : American Mathematical Soc.
ISBN 13 : 1470449005
Total Pages : 95 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Zeta and L -functions in Number Theory and Combinatorics by : Wen-Ching Winnie Li

Download or read book Zeta and L -functions in Number Theory and Combinatorics written by Wen-Ching Winnie Li and published by American Mathematical Soc.. This book was released on 2019-03-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-vanishing of L-Functions and Applications

Author : M. Ram Murty
Publisher : Springer Science & Business Media
ISBN 13 : 3034802749
Total Pages : 206 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Non-vanishing of L-Functions and Applications by : M. Ram Murty

Download or read book Non-vanishing of L-Functions and Applications written by M. Ram Murty and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.

Automorphic Forms, Representations, and L-functions

Author : Armand Borel
Publisher : American Mathematical Soc.
ISBN 13 : 082186792X
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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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 1977 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Eisenstein Series and Automorphic $L$-Functions

Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
ISBN 13 : 0821849891
Total Pages : 218 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Eisenstein Series and Automorphic $L$-Functions by : Freydoon Shahidi

Download or read book Eisenstein Series and Automorphic $L$-Functions written by Freydoon Shahidi and published by American Mathematical Soc.. This book was released on 2010 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.

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

Author : James W. Cogdell
Publisher : Walter de Gruyter
ISBN 13 : 3110892707
Total Pages : 441 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Automorphic Representations, L-Functions and Applications: Progress and Prospects by : James W. Cogdell

Download or read book Automorphic Representations, L-Functions and Applications: Progress and Prospects written by James W. Cogdell and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Arithmetic L-Functions and Differential Geometric Methods

Author : Pierre Charollois
Publisher : Springer Nature
ISBN 13 : 3030652033
Total Pages : 324 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Arithmetic L-Functions and Differential Geometric Methods by : Pierre Charollois

Download or read book Arithmetic L-Functions and Differential Geometric Methods written by Pierre Charollois and published by Springer Nature. This book was released on 2021-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Twisted L-Functions and Monodromy. (AM-150)

Author : Nicholas M. Katz
Publisher : Princeton University Press
ISBN 13 : 9780691091518
Total Pages : 262 pages
Book Rating : 4.0/5 (915 download)

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Book Synopsis Twisted L-Functions and Monodromy. (AM-150) by : Nicholas M. Katz

Download or read book Twisted L-Functions and Monodromy. (AM-150) written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2002-02-24 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.

Value-Distribution of L-Functions

Author : Jr̲n Steuding
Publisher : Springer Science & Business Media
ISBN 13 : 3540265260
Total Pages : 320 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Value-Distribution of L-Functions by : Jr̲n Steuding

Download or read book Value-Distribution of L-Functions written by Jr̲n Steuding and published by Springer Science & Business Media. This book was released on 2007-06-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiple Dirichlet Series, L-functions and Automorphic Forms

Author : Daniel Bump
Publisher : Springer
ISBN 13 : 0817683348
Total Pages : 367 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Multiple Dirichlet Series, L-functions and Automorphic Forms by : Daniel Bump

Download or read book Multiple Dirichlet Series, L-functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of L-functions

Author : Cristian Popescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821886983
Total Pages : 517 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Arithmetic of L-functions by : Cristian Popescu

Download or read book Arithmetic of L-functions written by Cristian Popescu and published by American Mathematical Soc.. This book was released on with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values

Author : Jianqiang Zhao
Publisher : World Scientific
ISBN 13 : 9814689416
Total Pages : 618 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values by : Jianqiang Zhao

Download or read book Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values written by Jianqiang Zhao and published by World Scientific. This book was released on 2016-03-07 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research.The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter.