These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews (MR) between 1984 and 1996. This is the third such set of volumes in number theory: The first was edited by W. J. LeVeque and included reviews from 1940-1972; the second was edited by R. K. Guy and appeared in 1984.

With the publication of the new review volumes, readers now have available reviews in number theory covering more than half a century.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

• Elementary number theory
• Sequences and sets
• Polynomials and matrices

• Diophantine equations
• Forms and linear algebraic groups
• Discontinuous groups and automorphic forms
• Arithmetic algebraic geometry (Diophantine geometry)

• Geometry of numbers
• Diophantine approximation, transcendental number theory
• Probabilistic theory: distribution modulo 1; metric theory of algorithms

• Exponential sums and character sums
• Zeta and $L$-functions: analytic theory
• Multiplicative number theory
• Additive number theory; partitions
• Other arithmetic-analytic topics

• Algebraic number theory: global fields
• Algebraic number theory: local and $p$-adic fields
• Finite fields and commutative rings (number-theoretic aspects)
• Connections with logic
• Computational number theory

• Preface
• Chapter Z General
• Classification scheme
• Subject word index
• Author index
• Key index
• MR number list
• Cyrillic table