Number Theory

Classically, higher logarithms appear as multivalued functions on the projective line. Today they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the "polylogarithm". The aim of the...

Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text...

The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be...

This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the...

In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on...

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method...

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2. Their congruence provided a unified setting for many congruences...

This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9783540129097Author D.V. ChudnovskyFormat PaperbackPage Count 309Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. KPublisher Springer-Verlag...

This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and...

George Andrews is one of the most influential figures in number theory and combinatorics. In the theory of partitions and q-hypergeometric series and in the study of Ramanujan's work, he is the unquestioned leader. To suitably honor him during his 70th...

This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar-including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a...

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new...

"Still waters run deep." This proverb expresses exactly how a mathematician Akihito Uchiyama and his works were. He was not celebrated except in the field of harmonic analysis, and indeed he never wanted that. He suddenly passed away in summer of 1997 at...

This volume includes articles spanning several research areas in number theory, such as arithmetic geometry, algebraic number theory, analytic number theory, and applications in cryptography and coding theory. Most of the articles are the results of...

the attention of The publication of Charles Pisot's thesis in 1938 brought to the mathematical community those marvelous numbers now known as the Pisot numbers (or the Pisot-Vijayaraghavan numbers). Although these numbers had been discovered earlier by A...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9783540099840Author S. MakiFormat PaperbackPage Count 201Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. KPublisher Springer-Verlag Berlin and...

Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically...

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number...

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic...

From the Preface by K. Chandrasekharan: "The publication of this collection of papers is intended as a service to the mathematical community, as well as a tribute to the genius of CARL LUDWIG SIEGEL. In the wide range of his interests, in his...

Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can...

This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs...

These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q). The problem of measuring the...

Cryptography is a key technology in electronic security systems. Modern cryptograpic techniques have many uses, such as to digitally sign documents, for access control, to implement electronic money, and for copyright protection. Because of these...

Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's...

From July 25-August 6, 1966 a Summer School on Local Fields was held in Driebergen (the Netherlands), organized by the Netherlands Universities Foundation for International Cooperation (NUFFIC) with financial support from NATO. The scientific organizing...

This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("Uber das quadratische Reciprocitatsgesetz. Eine vergleichende Darstellung der Beweise"), first published in 1885. It is divided...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9783540056416Author Hugh L. MontgomeryFormat PaperbackPage Count 178Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. KPublisher Springer-Verlag...

The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at least 2000 years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange,...

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including -invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9781466970762Author Louis KomzsikFormat PaperbackPage Count 120Imprint Trafford PublishingPublisher Trafford PublishingWeight(grams) 159g

The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9783662135372Author D.V. ChudnovskyFormat PaperbackPage Count 309Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. KPublisher Springer-Verlag...

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes."...

The Hardy-Littlewood circle method was invented a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of...

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo- metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the...

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including -invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's...

This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and...

We begin by making clear the meaning of the term "tame". The higher ramifi cation groups, on the one hand, and the one-units of chain groups, on the other, are to lie in the kernels of the respective representations considered. We shall...