Contributions To The Theory Of Zeta Functions The Modular Relation Supremacy
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| Author | : Shigeru Kanemitsu |
| Publisher | : World Scientific |
| Total Pages | : 316 |
| Release | : 2014-12-15 |
| Genre | : Mathematics |
| ISBN | : 9814449636 |
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.
| Author | : George E Andrews |
| Publisher | : World Scientific |
| Total Pages | : 704 |
| Release | : 2024-08-19 |
| Genre | : Mathematics |
| ISBN | : 9811277389 |
This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.
| Author | : Wenpeng Zhang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 247 |
| Release | : 2006-06-05 |
| Genre | : Mathematics |
| ISBN | : 0387308296 |
This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.
| Author | : Jianya Liu |
| Publisher | : World Scientific |
| Total Pages | : 268 |
| Release | : 2007-07-05 |
| Genre | : Mathematics |
| ISBN | : 9814474878 |
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.
| Author | : Shigeru Kanemitsu |
| Publisher | : World Scientific |
| Total Pages | : 212 |
| Release | : 2015-02-10 |
| Genre | : Mathematics |
| ISBN | : 9814644943 |
Based on the successful 7th China-Japan seminar on number theory conducted in Kyushu University, this volume is a compilation of survey and semi-survey type of papers by the participants of the seminar. The topics covered range from traditional analytic number theory to elliptic curves and universality. This volume contains new developments in the field of number theory from recent years and it provides suitable problems for possible new research at a level which is not unattainable. Timely surveys will be beneficial to a new generation of researchers as a source of information and these provide a glimpse at the state-of-the-art affairs in the fields of their research interests.
| Author | : Jianqiang Zhao |
| Publisher | : World Scientific |
| Total Pages | : 618 |
| Release | : 2016-03-07 |
| Genre | : Mathematics |
| ISBN | : 9814689416 |
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.
| Author | : Haruzo Hida |
| Publisher | : World Scientific |
| Total Pages | : 446 |
| Release | : 2021-10-04 |
| Genre | : Mathematics |
| ISBN | : 9811241384 |
This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows:Many open problems are presented to stimulate young researchers pursuing their field of study.
| Author | : Pradip Debnath |
| Publisher | : CRC Press |
| Total Pages | : 493 |
| Release | : 2023-10-17 |
| Genre | : Mathematics |
| ISBN | : 1000967263 |
Advanced Mathematical Analysis and its Applications presents state-of-the-art developments in mathematical analysis through new and original contributions and surveys, with a particular emphasis on applications in engineering and mathematical sciences. New research directions are indicated in each of the chapters, and while this book is meant primarily for graduate students, there is content that will be equally useful and stimulating for faculty and researchers. The readers of this book will require minimum knowledge of real, complex, and functional analysis, and topology. Features Suitable as a reference for graduate students, researchers, and faculty Contains the most up-to-date developments at the time of writing.
| Author | : Toyokazu Hiramatsu |
| Publisher | : World Scientific |
| Total Pages | : 188 |
| Release | : 2016-09-13 |
| Genre | : Mathematics |
| ISBN | : 9813142286 |
This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.
| Author | : Masayoshi Hata |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 376 |
| Release | : 2016-12-12 |
| Genre | : Mathematics |
| ISBN | : 9813142847 |
This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis.
