Number theory

This definitive synthesis of mathematician Gregory Margulis's research brings together leading experts to cover the breadth and diversity of disciplines Margulis's work touches upon.

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures.

The book intends to give a modern presentation of the classical Markov and Lagrange spectrum, which are fundamental objects from the theory of Diophantine approximations and of their several generalizations related to Dynamical Systems and Differential Geometry.

With this translation, the classic monograph Uber die Klassenzahl abelscher Zahlkorper by Helmut Hasse is now available in English for the first time.

The continuation of an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Bedlewo, Poland in September 2015.

This book is devoted to algebraic models and their applications.

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics.

This book develops a new theory in convex geometry, generalizing positive bases and related to Caratheordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization.

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes.

This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory.

A treatment of cutting-edge research on the distribution modulo one of sequences and related topics, with exercises and open problems.

The last one hundred years have seen many important achievements in the classical part of number theory.

Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians.

This book is devoted to algebraic models and their applications.

Curvature and Homology

Covers extensions of Buchberger''s Theory and Algorithm, and promising recent alternatives to Gröbner bases.

Critical Point Theory in Global Analysis and Differential Topology

In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H.

Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Edouard Lucas between 1876 and 1880, that they are now named after him.

Praise for the First Edition beautiful and well worth the reading with many exercises and a good bibliography, this book will fascinate both students and teachers.

Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory.

This textbook is a practical yet in depth guide to cryptography and its principles and practices.

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including ?

This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics.

This book is an outgrowth of the special term "e;Harmonic Analysis, Representation Theory, and Integral Geometry,"e; held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied.

The main topics of this volume, dedicated to Lance Littlejohn, are operator and spectral theory, orthogonal polynomials, combinatorics, number theory, and the various interplays of these subjects.

P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field.

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed.

The second edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?

Chord Transformations in Higher-Dimensional Networks proposes an in-depth formal framework for generalized Tonnetze.

Volume 2 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Three major branches of number theory are included in the volume: namely analytic number theory, algebraic number theory, and transcendental number theory.

This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A.

This book is purely algebraic and concentrates on cyclic homology rather than on cohomology.

The chapters in this contributed volume explore new results and existing problems in algebra, analysis, and related topics.

This book can be seen as a continuation of Equations and Inequalities: El- ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series.

Decompositions of Manifolds

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals.

An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.

Positive Operators

Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing.