Zeta Functions Topology And Quantum Physics

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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 Topology And Quantum Physics

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Author : Takashi Aoki
language : en
Publisher: Springer
Release Date : 2008-11-01

Zeta Functions Topology And Quantum Physics written by Takashi Aoki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 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.

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.

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.

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.

Computer Algebra In Quantum Field Theory

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Author : Carsten Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-05

Computer Algebra In Quantum Field Theory written by Carsten Schneider 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 2013-10-05 with Science categories.

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

A Combinatorial Perspective On Quantum Field Theory

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Author : Karen Yeats
language : en
Publisher: Springer
Release Date : 2016-11-23

A Combinatorial Perspective On Quantum Field Theory written by Karen Yeats and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-23 with Science categories.

This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.

Number Theory Dreaming In Dreams Proceedings Of The 5th China Japan Seminar

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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2009-11-26

Number Theory Dreaming In Dreams Proceedings Of The 5th China Japan Seminar 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 2009-11-26 with Mathematics categories.

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory — quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms — Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi-Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.

Number Theory

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Author : Takashi Aoki
language : en
Publisher: World Scientific
Release Date : 2010

Number Theory written by Takashi Aoki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory ? quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms ? Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi?Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.

Number Theory Sailing On The Sea Of Number Theory Proceedings Of The 4th China Japan Seminar

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Author : Jianya Liu
language : en
Publisher: World Scientific
Release Date : 2007-07-05

Number Theory Sailing On The Sea Of Number Theory Proceedings Of The 4th China Japan Seminar written by Jianya Liu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Mathematics categories.

This volume is not an ordinary proceedings volume assembling papers submitted but a collection of prestigious survey papers on various subjects studied enthusiastically by experts all over the world. The reader will uncover profound, new research problems as well as numerous signposts for future direction.