On The Global Theory Of Shintani Zeta Functions
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Shintani Zeta Functions
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Author : Akihiko Yukie
language : en
Publisher: Cambridge University Press
Release Date : 1993
Shintani Zeta Functions written by Akihiko Yukie and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function. This book will be of great interest to all serious workers in analytic number theory.
On The Global Theory Of Shintani Zeta Functions
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Author : Akihiko Yukie
language : de
Publisher:
Release Date : 1991
On The Global Theory Of Shintani Zeta Functions written by Akihiko Yukie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
On The Global Theory Of Shintani Zeta Functions
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Author : Akihiko Yukie
language : de
Publisher:
Release Date : 1991
On The Global Theory Of Shintani Zeta Functions written by Akihiko Yukie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
On The Global Theory Of Shintani Zeta Functions
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Author : A. Yukie
language : en
Publisher:
Release Date : 1991
On The Global Theory Of Shintani Zeta Functions written by A. Yukie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
A Tribute To Emil Grosswald Number Theory And Related Analysis
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Author : Marvin Isadore Knopp
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
A Tribute To Emil Grosswald Number Theory And Related Analysis written by Marvin Isadore Knopp 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 1993 with Mathematics categories.
Emil Grosswald was a mathematician of great accomplishment and remarkable breadth of vision. This volume pays tribute to the span of his mathematical interests, which is reflected in the wide range of papers collected here. With contributions by leading contemporary researchers in number theory, modular functions, combinatorics, and related analysis, this book will interest graduate students and specialists in these fields. The high quality of the articles and their close connection to current research trends make this volume a must for any mathematics library.
Contributions To The Theory Of Zeta Functions
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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2014-12-15
Contributions To The Theory Of Zeta Functions written by Shigeru Kanemitsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Mathematics categories.
This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
Geometric Aspects Of The Trace Formula
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Author : Werner Müller
language : en
Publisher: Springer
Release Date : 2018-10-11
Geometric Aspects Of The Trace Formula written by Werner Müller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-11 with Mathematics categories.
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.
Introduction To Prehomogeneous Vector Spaces
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Author : Tatsuo Kimura
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Introduction To Prehomogeneous Vector Spaces written by Tatsuo Kimura 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 2003 with Mathematics categories.
This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. The subject combines elements of several areas of mathematics, such as algebraic geometry, Lie groups, analysis, number theory, and invariant theory. An important objective is to create applications to number theory. For example, one of the key topics is that of zeta functions attached to prehomogeneous vector spaces; these are generalizations of the Riemann zeta function, a cornerstone of analytic number theory. Prehomogeneous vector spaces are also of use in representation theory, algebraic geometry and invariant theory. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces and a classification theory of irreducible prehomogeneous vector spaces. It strives, and to a large extent succeeds, in making this content, which is by its nature fairly technical, self-contained and accessible. The first section of the book, "Overview of the theory and contents of this book," Is particularly noteworthy as an excellent introduction to the subject.
Combinatorial Number Theory
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Author : Bruce Landman
language : en
Publisher: Walter de Gruyter
Release Date : 2013-08-29
Combinatorial Number Theory written by Bruce Landman and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-29 with Mathematics categories.
This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.
The Theory Of Zeta Functions Of Root Systems
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Author : Yasushi Komori
language : en
Publisher: Springer Nature
Release Date : 2024-01-02
The Theory Of Zeta Functions Of Root Systems written by Yasushi Komori and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-02 with Mathematics categories.
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.