Superb study of one of the most influential classics in mathematics examines the landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics.
Here's a sample of other books in this Dover category
Algebraic Number Theory by Edwin Weiss Ideal either for classroom use or as exercises for mathematically-minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.
Number Theory by George E. Andrews Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more
The Riemann Zeta-Function: Theory and Applications by Aleksandar Ivic This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.
The Variational Theory of Geodesics by M. M. Postnikov Compact, self-contained text by noted theorist presents the most fundamental aspects of modern differential geometry as well as the basic tools required for the study of Morse theory. 1967 edition.
Introduction to the Theory of Numbers by Harold N. Shapiro Starting with the fundamentals, this text advances to an intermediate level. Geared toward advanced undergraduates and graduate students, it covers congruence, counting problems, and prime number theory. 1983 edition.
Fourier Analysis in Several Complex Variables by Leon Ehrenpreis Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
The Concept of a Riemann Surface by Hermann Weyl, Gerald R. MacLane This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
