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

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