Number Theory: Arithmetic In Shangri-la - Proceedings Of The 6th China-japan Seminar

Number Theory: Arithmetic In Shangri-la - Proceedings Of The 6th China-japan Seminar
Title Number Theory: Arithmetic In Shangri-la - Proceedings Of The 6th China-japan Seminar PDF eBook
Author Shigeru Kanemitsu
Publisher World Scientific
Pages 273
Release 2013-02-20
Genre Mathematics
ISBN 9814452467

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This volume is based on the successful 6th China-Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series.

Number Theory: Plowing And Starring Through High Wave Forms - Proceedings Of The 7th China-japan Seminar

Number Theory: Plowing And Starring Through High Wave Forms - Proceedings Of The 7th China-japan Seminar
Title Number Theory: Plowing And Starring Through High Wave Forms - Proceedings Of The 7th China-japan Seminar PDF eBook
Author Shigeru Kanemitsu
Publisher World Scientific
Pages 212
Release 2015-02-10
Genre Mathematics
ISBN 9814644943

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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.

Neurons: A Mathematical Ignition

Neurons: A Mathematical Ignition
Title Neurons: A Mathematical Ignition PDF eBook
Author Masayoshi Hata
Publisher World Scientific
Pages 231
Release 2014-09-16
Genre Mathematics
ISBN 9814618632

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This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine. The detailed analysis from a viewpoint of “dynamical systems”, even in a single neuron case, enables us to obtain amazingly good rational approximations to the Hecke-Mahler series with two variables. Some interesting numerical applications of our rational approximations are also discussed.This book is fundamentally self-contained and many topics required in it are explained from the beginning. Each chapter contains a number of instructive and mostly original exercises at various levels.

Introduction To Non-abelian Class Field Theory, An: Automorphic Forms Of Weight 1 And 2-dimensional Galois Representations

Introduction To Non-abelian Class Field Theory, An: Automorphic Forms Of Weight 1 And 2-dimensional Galois Representations
Title Introduction To Non-abelian Class Field Theory, An: Automorphic Forms Of Weight 1 And 2-dimensional Galois Representations PDF eBook
Author Toyokazu Hiramatsu
Publisher World Scientific
Pages 188
Release 2016-09-13
Genre Mathematics
ISBN 9813142286

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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.

Contributions to the Theory of Zeta-Functions

Contributions to the Theory of Zeta-Functions
Title Contributions to the Theory of Zeta-Functions PDF eBook
Author Shigeru Kanemitsu
Publisher World Scientific
Pages 316
Release 2014-12-15
Genre Mathematics
ISBN 9814449628

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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.

Algorithms and Complexity in Mathematics, Epistemology, and Science

Algorithms and Complexity in Mathematics, Epistemology, and Science
Title Algorithms and Complexity in Mathematics, Epistemology, and Science PDF eBook
Author Nicolas Fillion
Publisher Springer
Pages 300
Release 2019-02-07
Genre Mathematics
ISBN 1493990519

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ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values
Title Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values PDF eBook
Author Jianqiang Zhao
Publisher World Scientific
Pages 618
Release 2016-03-07
Genre Mathematics
ISBN 9814689416

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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.