Stopple Jeffrey. A Primer of Analytic Number Theory: From Pythagoras to Riemann

Cambridge University Press, 2003. — 400 p. — ISBN10: 0521012538; ISBN13: 978-0521012539.This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. The author pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems (some of which have million dollar prizes). The capstone of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.