Excursions in Multiplicative Number Theory

Table of Contents

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   Book Overview
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   Chapter 1 Arithmetic Convolution
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   Chapter 2 A Calculus on Arithmetical Functions
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   Chapter 3 Analytical Dirichlet Series
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   Chapter 4 Growth of Arithmetical Functions
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   Chapter 5 An “Algebraical” Multiplicative Function
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   Chapter 6 Möbius Inversions
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   Chapter 7 Handling a Smooth Factor
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   Chapter 8 The Convolution Method
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    Chapter 9 Euler Products and Euler Sums
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    Chapter 10 Some Practice
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    Chapter 11 Dirichlet’s Hyperbola Principle
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    Chapter 12 The Mertens Estimates
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    Chapter 13 The Levin–Faĭnleĭb Theorem and Analogues
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    Chapter 14 Variations on a Theme of Chebyshev
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    Chapter 15 Primes in Arithmetical Progressions
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    Chapter 16 Computing a Famous Constant
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    Chapter 17 Euler Products with Primes in Progressions
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    Chapter 18 The Chinese Remainder Theorem and Multiplicativity
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    Chapter 19 The Riemann Zeta Function
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    Chapter 20 The Mellin Transform
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    Chapter 21 Proof of Theorem $$\mathscr {C}$$ C
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    Chapter 22 Roughing up: Removing a Smoothening
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    Chapter 23 Proving the Prime Number Theorem
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    Chapter 24 The Selberg Formula
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    Chapter 25 Rankin’s Trick and Brun’s Sieve
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    Chapter 26 Three Arithmetical Exponential Sums
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    Chapter 27 Convolution Method and Non-Positive Functions
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    Chapter 28 The Large Sieve Inequality
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    Chapter 29 Montgomery’s Sieve