From Arithmetic To Zeta Functions

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From Arithmetic To Zeta Functions

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Author : Jürgen Sander
language : en
Publisher: Springer
Release Date : 2016-12-29

From Arithmetic To Zeta Functions written by Jürgen Sander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-29 with Mathematics categories.

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

Dynamical Spectral And Arithmetic Zeta Functions

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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Dynamical Spectral And Arithmetic Zeta Functions written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Functions, Zeta categories.

The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.

Zeta Functions Of Groups And Rings

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Author : Marcus du Sautoy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008

Zeta Functions Of Groups And Rings written by Marcus du Sautoy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Zeta functions have been a powerful tool in mathematics over the last two centuries. This book considers a new class of non-commutative zeta functions which encode the structure of the subgroup lattice in infinite groups. The book explores the analytic behaviour of these functions together with an investigation of functional equations. Many important examples of zeta functions are calculated and recorded providing an important data base of explicit examples and methods for calculation.

Zeta Functions Over Zeros Of Zeta Functions

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Author : André Voros
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-21

Zeta Functions Over Zeros Of Zeta Functions written by André Voros and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-21 with Mathematics categories.

In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.

Zeta Functions Topology And Quantum Physics

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Author : Takashi Aoki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-10

Zeta Functions Topology And Quantum Physics written by Takashi Aoki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-10 with Mathematics categories.

This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Zeta Functions In Algebra And Geometry

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Author : Antonio Campillo
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Zeta Functions In Algebra And Geometry written by Antonio Campillo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Algebraic varieties categories.

The volume contains the proceedings of the ``Second International Workshop on Zeta Functions in Algebra and Geometry'' held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).

Zeta Functions Of Reductive Groups And Their Zeros

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Author : Weng Lin
language : en
Publisher: World Scientific
Release Date : 2018-02-07

Zeta Functions Of Reductive Groups And Their Zeros written by Weng Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-07 with Mathematics categories.

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

The Theory Of The Riemann Zeta Function

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Author : Late Savilian Professor of Geometry E C Titchmarsh
language : en
Publisher: Oxford University Press
Release Date : 1986

The Theory Of The Riemann Zeta Function written by Late Savilian Professor of Geometry E C Titchmarsh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

The Lerch Zeta Function

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Author : Antanas Laurincikas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

The Lerch Zeta Function written by Antanas Laurincikas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions. The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph Limit Theorems for the Riemann zeta-function. This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students.

History Of Zeta Functions

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Author : Robert Spira
language : en
Publisher:
Release Date : 1999

History Of Zeta Functions written by Robert Spira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Functions, Zeta categories.