xiv Acknowledgments

Beyond these works that I have mainly relied on for this book, there

are many other excellent treatments of analytic number theory. It may be

appropriate at this point to mention a few that are particularly important

for one reason or another. Introduction to Analytic Number Theory by Tom

M. Apostol [Apo76] has for decades been the most widely used introduc-

tory text. It carefully develops material needed from elementary number

theory rather than assuming it as a prerequisite, and has many exercises.

Multiplicative Number Theory by Harold Davenport [Dav00] is a classic ac-

count of the distribution of primes in arithmetic progressions. It has been

in print for more than forty years, and is still one of the more frequently

assigned textbooks for courses in analytic number theory. Analytic Number

Theory by Henryk Iwaniec [IK04] and Emmanuel Kowalski is a broad, deep

and modern treatment. Of outstanding importance to the development of

analytic number theory in its early stages was Handbuch Der Lehre von der

Verteilung der Primzahlen [Lan74] by Edmund Landau.

For information on the historical background I have in addition relied

on these sources: Gauss and Jacobi Sums [BEW98] by B. C. Berndt,

R. J. Evans and K. S. Williams, Pioneers of Representation Theory: Frobe-

nius, Burnside, Schur, and Brauer [Cur99] by C. W. Curtis, the survey

paper [DE80] by H. G. Diamond on elementary methods in prime num-

ber theory, History of the Theory of Numbers [Dic34] by L. E. Dickson,

Riemann’s Zeta Function [Edw01] by H. M. Edwards, the sixth edition of

An Introduction to the Theory of Numbers [HW08] by G. H. Hardy and

E. M. Wright and revised by D. R. Heath-Brown and J. H. Silverman, the

introductory notes by H. A. Heilbronn in volume I of the Collected Papers

of G. H. Hardy [Har66], the 1990 edition of The Distribution of Prime

Numbers [Ing90] by A. E. Ingham and with a Foreword by R. C. Vaughan,

Multiplicative Number Theory I. Classical Theory [MV07] by H. L. Mont-

gomery and R. C. Vaughan, and The Development of Prime Number Theory

[Nar00a] by W. Narkiewicz, and the survey paper [VW02] on Waring’s

Problem by R. C. Vaughan and T. D. Wooley.

All figures have been made with InkscapeTM and MathematicaTM.

Marius Overholt