This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

Readership

Analytic number theorists and harmonic analysts.

Reviews

"The book is a masterpiece of exposition and can be highly recommended to anybody interested in the connections of analysis and number theory."

-- Zentralblatt MATH

"Many analysts, not necessarily specialists in harmonic analysis, will be able to find much to interest them here ... The long lists of references provided for each chapter are one of the invaluable features of a very readable and stimulating book."

-- Bulletin of the LMS

"These lectures give a lively, often original, look at a selection of topics from the area described by the title and, once one accepts the restriction of the previous sentence, there is nobody, anywhere, better equipped to tell this tale ... this book deserves the attention of every analytic number theorist ... adds considerably more to the literature than a number of books which could serve that function."

-- Mathematical Reviews

Table of Contents

• Uniform distribution
• van der Corput sets
• Exponential sums I: The methods of Weyl and van der Corput
• Exponential sums II: Vinogradov's method
• An introduction to Turán's method
• Irregularities of distribution
• Mean and large values of Dirichlet polynomials
• Distribution of reduced residue classes in short intervals
• Zeros of $L$-functions
• Small polynomials with integral coefficients
• Some unsolved problems
• Index