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Analytic Number Theory

Table of Contents

• Introduction and Dedication

1. The Idea of Analytic Number Theory
   • Addition Problems
   • Change Making
   • Crazy Dice
   • Can r(n) be “constant?”
   • A Splitting Problem
   • An Identity of Euler’s
   • Marks on a Ruler
   • Dissection into Arithmetic Progressions
2. The Partition Function
   • The Generating Function
   • The Approximation
   • Riemann Sums
   • The Coefficients of q(n)
3. The Erdös–Fuchs Theorem
   • Erdös–Fuchs Theorem
4. Sequences without Arithmetic Progressions
   • The Basic Approximation Lemma
5. The Waring Problem
6. A “Natural” Proof of the Nonvanishing of L-Series
7. Simple Analytic Proof of the Prime Number Theorem
   • First Proof of the Prime Number Theorem
   • Second Proof of the Prime Number Theorem

• Index

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