Contents
Preface ix
Chapter 1. Introduction 1
§1.1. Notation and Arithmetical Functions 1
§1.2. What are ^-Series and Theta Functions? 6
§1.3. Fundamental Theorems about g-Series and Theta
Functions 7
§1.4. Notes 22
Chapter 2. Congruences for p(n) and r(n) 27
§2.1. Historical Background 27
§2.2. Elementary Congruences for r{n) 28
§2.3. Ramanujan's Congruence p(5n -f 4) = 0 (mod 5) 31
§2.4. Ramanujan's Congruence p(7n + 5) = 0 (mod 7) 39
§2.5. The Parity of p(n) 43
§2.6. Notes 49
Chapter 3. Sums of Squares and Sums of Triangular Numbers 55
§3.1. Lambert Series 55
§3.2. Sums of Two Squares 56
§3.3. Sums of Four Squares 59
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