Contents
Preface ix
Notation xiii
Frequently Used Functions xvii
Chapter 1. Preliminary Notions 1
§1.1. Approximating a sum by an integral 1
§1.2. The Euler-MacLaurin formula 2
§1.3. The Abel summation formula 5
§1.4. Stieltjes integrals 7
§1.5. Slowly oscillating functions 8
§1.6. Combinatorial results 9
§1.7. The Chinese Remainder Theorem 10
§1.8. The density of a set of integers 11
§1.9. The Stirling formula 11
§1.10. Basic inequalities 13
Problems on Chapter 1 15
Chapter 2. Prime Numbers and Their Properties 19
§2.1. Prime numbers and their polynomial representations 19
§2.2. There exist infinitely many primes 21
§2.3. A first glimpse at the size of π(x) 21
§2.4. Fermat numbers 22
§2.5. A better lower bound for π(x) 24
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