Multiplicative Number Theory

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ISBN: 978-1-4757-5929-7 (Print) 978-1-4757-5927-3 (Online)

Table of contents (30 chapters)

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  1. Front Matter

    Pages i-xiii

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    Book Chapter

    Pages 1-11

    Primes in Arithmetic Progression

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    Book Chapter

    Pages 12-16

    Gauss’ Sum

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    Pages 17-26

    Cyclotomy

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    Pages 27-34

    Primes in Arithmetic Progression: The General Modulus

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    Book Chapter

    Pages 35-42

    Primitive Characters

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    Pages 43-53

    Dirichlet’s Class Number Formula

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    Pages 54-58

    The Distribution of the Primes

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    Book Chapter

    Pages 59-64

    Riemann’s Memoir

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    Book Chapter

    Pages 65-72

    The Functional Equation of the L Functions

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    Book Chapter

    Pages 73-73

    Properties of the Γ Function

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    Book Chapter

    Pages 74-78

    Integral Functions of Order 1

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    Book Chapter

    Pages 79-83

    The Infinite Products for ξ(s) and ξ(s, χ)

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    Pages 84-87

    A Zero-Free Region for ζ(s)

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    Pages 88-96

    Zero-Free Regions for L(s, χ)

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    Book Chapter

    Pages 97-100

    The Number N(T)

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    Pages 101-103

    The Number N(T, χ)

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    Book Chapter

    Pages 104-110

    The Explicit Formula for Ψ(x)

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    Book Chapter

    Pages 111-114

    The Prime Number Theorem

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    Book Chapter

    Pages 115-120

    The Explicit Formula for ψ(x, χ)

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    Book Chapter

    Pages 121-125

    The Prime Number Theorem for Arithmetic Progressions (I)

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