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Primary References......Page 7 I Analytic Number Theory......Page 16 Introduction......Page 18 There are Infinitely Many Primes......Page 19 Euclid and his Imitators......Page 20 Coprime Integer Sequences......Page 21 The Riemann Zeta Function......Page 23 Squarefree Numbers......Page 28 Smooth Numbers......Page 31 The Heavy Machinery......Page 33 Exercises......Page 34 An Empirical Approach......Page 36 Exercises: Some Consequences of the PNT......Page 39 The Primes are Infinitely Fewer than the Integers......Page 40 More Primes than Squares......Page 42 Chebyshev's Work on pi(x)......Page 43 Proof of Theorem 1.5.1......Page 46 Proof of Theorem 1.5.2......Page 47 Proof of Bertrand's Postulate......Page 48 Exercises......Page 49 Polynomials that Represent Many Primes......Page 52 Mertens' Theorem, sans the Constant......Page 54 The Constant in Mertens' Theorem......Page 57 Exercises......Page 60 Primes in Arithmetic Progressions......Page 61 The Twin Prime and Goldbach Problems......Page 62 An Extended Hardy-Littlewood Conjecture......Page 64 Exercises: More on the Bateman-Horn Conjecture......Page 66 The Prime Ideal Theorem......Page 67 Chebyshev Analogs......Page 68 Exercises....

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Author

Pollack P.

Published

2004

Language

EN

Category

nonfiction

Subjects

Mathematics, Combinatorics, Stem