A Primer of Analytic Number Theory

This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple 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. The culmination 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.

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Chapters
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01 - Sums And Differences
02 - Products And Divisibility
03 - Order Of Magnitude
04 - Averages
05 - Primes
06 - Basel Problem
07 - Euler's Product
08 - The Riemann Zeta Function
09 - Symmetry
10 - Explicit Formula
11 - Pell's Equation
12 - Elliptic Curves
13 - Analytic Theory Of Algebraic Equations