Number Theory Plowing And Starring Through High Wave Forms Proceedings Of The 7th China Japan Seminar
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Number Theory Plowing And Starring Through High Wave Forms Proceedings Of The 7th China Japan Seminar
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Author : Shigeru Kanemitsu
language : en
Publisher: World Scientific
Release Date : 2015-02-10
Number Theory Plowing And Starring Through High Wave Forms Proceedings Of The 7th 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 2015-02-10 with Mathematics categories.
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.
Introduction To Non Abelian Class Field Theory An Automorphic Forms Of Weight 1 And 2 Dimensional Galois Representations
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Author : Toyokazu Hiramatsu
language : en
Publisher: World Scientific
Release Date : 2016-09-13
Introduction To Non Abelian Class Field Theory An Automorphic Forms Of Weight 1 And 2 Dimensional Galois Representations written by Toyokazu Hiramatsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-13 with Mathematics categories.
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.
Multiple Zeta Functions Multiple Polylogarithms And Their Special Values
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Author : Jianqiang Zhao
language : en
Publisher: World Scientific
Release Date : 2016-03-07
Multiple Zeta Functions Multiple Polylogarithms And Their Special Values written by Jianqiang Zhao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Mathematics categories.
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.
Problems And Solutions In Real Analysis Second Edition
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Author : Masayoshi Hata
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-12-12
Problems And Solutions In Real Analysis Second Edition written by Masayoshi Hata and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-12 with Mathematics categories.
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.
Combinatorial And Additive Number Theory Ii
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer
Release Date : 2018-01-13
Combinatorial And Additive Number Theory Ii written by Melvyn B. Nathanson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-13 with Mathematics categories.
Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling.
Elementary Modular Iwasawa Theory
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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2021-10-04
Elementary Modular Iwasawa Theory written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-04 with Mathematics categories.
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.
Derived Langlands Monomial Resolutions Of Admissible Representations
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Author : Victor P Snaith
language : en
Publisher: World Scientific
Release Date : 2018-12-06
Derived Langlands Monomial Resolutions Of Admissible Representations written by Victor P Snaith and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-06 with Mathematics categories.
The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.
The Vertical Generalization Of Goldbach S Conjecture An Infinite Class Of Conjectures Stronger Than Goldbach S
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Author : Andrei-Lucian Drăgoi
language : en
Publisher: Dr. Andrei-Lucian Drăgoi
Release Date : 2021-07-30
The Vertical Generalization Of Goldbach S Conjecture An Infinite Class Of Conjectures Stronger Than Goldbach S written by Andrei-Lucian Drăgoi and has been published by Dr. Andrei-Lucian Drăgoi this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-30 with Mathematics categories.
This work proposes the generalization of the binary (strong) Goldbach’s Conjecture, briefly called “the Vertical Binary Goldbach’s Conjecture”, which is essentially a meta-conjecture because it states an infinite number of conjectures stronger than Goldbach’s, which all apply on “iterative” primes with recursive prime indexes, with many potential theoretical and practical applications in mathematics and physics) and a very special self-similar property of the primes subset of positive integers.
Number Theory
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Author : Kağan Kurşungöz
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-08
Number Theory written by Kağan Kurşungöz and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-08 with Mathematics categories.
Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory. Original research is presented that discusses modern techniques and survey papers from selected academic scholars.
The Vertical Generalization Of The Binary Goldbach S Conjecture As Applied On Iterative Primes With Recursive Prime Indexes I Primeths
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Author : Andrei-Lucian Drăgoi
language : en
Publisher: Infinite Study
Release Date :
The Vertical Generalization Of The Binary Goldbach S Conjecture As Applied On Iterative Primes With Recursive Prime Indexes I Primeths written by Andrei-Lucian Drăgoi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This article proposes a synthesized classification of some Goldbach-like conjectures, including those which are “stronger” than the Binary Goldbach’s Conjecture (BGC) and launches a new generalization of BGC briefly called “the Vertical Binary Goldbach’s Conjecture” (VBGC), which is essentially a metaconjecture, as VBGC states an infinite number of conjectures stronger than BGC, which all apply on “iterative” primes with recursive prime indexes (i-primeths).