Product Description: This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals...read more

Product Description: This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application...read more

Product Description: We use addition on a daily basis―yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems...read more

Product Description: "A very welcome addition to books on number theory."—Bulletin, American Mathematical SocietyClear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working knowledge of calculus...read more

This book is a systematic introduction to analytic methods in number theory, and assumes as a prerequisite only what is taught in a standard undergraduate course. The author aids readers by including a section of bibliographic notes and detailed exercises at the end of each chapter. Tenenbaum has emphasized methods rather than results, so readers should be able to tackle more advanced material than is included here. Moreover, he covers developments on many new and unpublished topics, such as: the Selberg-Delange method; a version of the Ikehara-Ingham Tauberian theorem; and a detailed exposition of the arithmetical use of the saddle-point method.

Product Description: Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries...read more

Product Description: Properties aren t magic! They are special rules that numbers follow so you can solve problems quickly in your head. Using detailed instructions and rhythmic text, students gain understanding of when and how to use mathematical properties...read more

Product Description: This book is about the theory and practice of integer factorization presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms...read more

Product Description: The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (1953-2011), whose seminal thesis is published here for the first time...read more

Product Description: The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz)...read more

Product Description: This volume contains the proceedings of the International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, held November 13-18, 2011, at the Banff International Research Station, Banff, Alberta, Canada...read more

Product Description: This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics.   This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties...read more

Product Description: This collection of eighteen papers and eleven commentaries by noted economists, demographers, and sociologists, combines systematic discussions of the demographic effects of below-replacement fertility with efforts to explain its social origins, to determine the likely societal consequences and to assess potential policy responses...read more

Product Description: This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.