Number theory Books

This book is an outgrowth of the conference "Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods" that was held in Paris in May 2016. Gathering contributions by leading experts in the field...

This volume explores the rich interplay between number theory and wireless communications, reviewing the surprisingly deep connections between these fields and presenting new research directions to inspire future research. The contributions of this...

This self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes,...

This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas...

Combinatorial research has proceeded vigorously in Russia over the last few decades, based on both translated Western sources and original Russian material. The present volume extends the extremal approach to the solution of...

'Et moi, ... , si j'avait su comment en revcnrr, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back. Jules Verne where it belongs, on the topmost shelf next to the dusty...

Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his...

Uchiyama's decomposition of BMO functions is considered the "Mount Everest of Hardy space theory". This book is based on the draft, which the author completed before his sudden death in 1997. Nowadays, his contributions are...

The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic...

Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers...

As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the...

This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.The mathematical theory of VOAs...

The numerous explicit formulae of the classical theory of quadratic forms revealed remarkable multiplicative properties of the numbers of integral representations of integers by positive definite integral quadratic forms. These...

For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with...

In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth 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...

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate...

In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its...

​Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix...

This introduction to cryptography employs a programming-oriented approach to study the most important cryptographic schemes in current use and the main cryptanalytic attacks against them. Discussion of the theoretical aspects, emphasizing precise...

This volume, as Andrew M. Odlzyko writes in the foreword, "commemorates and celebrates the life and achievements of an extraordinary person." Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has...

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number...

A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up...

The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti­ cal Physics. The first part is mathematically oriented; it deals...

This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves...

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...

Lattices are discrete subgroups of maximal rank in a Euclidean space. To each such geometrical object, we can attach a canonical sphere packing which, assuming some regularity, has a density. The question of estimating the...

Examensarbeit aus dem Jahr 2009 im Fachbereich Mathematik - Zahlentheorie, Note: 1, Universität Regensburg, Sprache: Deutsch, Abstract: Wann der Begriff der Primzahl in der Geschichte der Mathematik das erste Mal aufgetaucht ist, scheint nicht ganz...

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder [40] and Laumon [62]. In writing this text based on a...

On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum...

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic...

1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen­ ta, where we find a proof of their infinitude, now regarded as...

Introduction Model theorists have often joked in recent years that the part of mathemat­ ical logic known as "pure model theory" (or stability theory), as opposed to the older and more traditional "model theory applied to...

The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A...

In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations...

The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way,...

Before his untimely death in 1986, Alain Durand had undertaken a systematic and in-depth study of the arithmetic perspectives of polynomials. Four unpublished articles of his, formed the centerpiece of attention at a colloquium...

It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality...

These notes give an account of recent work in harmonic analysis dealing with the analytical foundations of A. Weil's theory of metaplectic groups. It is shown that Weil's main theorem holds for a class of functions (a certain...

Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory. This book lays foundations for a theory of capacity for adelic sets on algebraic curves. Its main result is...

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

The problem of uniform distribution of sequences initiated by Hardy, Little­ wood and Weyl in the 1910's has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called...

In gratefuZ remerribrance of Marston Morse and John von Neumann This text formed the basis of an optional course of lectures I gave in German at the Swiss Federal Institute of Technology (ETH), Zlirich, during the ...