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Topics in Analytic Number Theory

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Cover of 'Topics in Analytic Number Theory'

Table of Contents

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    Book Overview
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    Chapter 1 Bernoulli Polynomials and Bernoulli Numbers
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    Chapter 2 The Euler-MacLaurin Sum Formula
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    Chapter 3 The Γ -function and Mellin’s Theorem
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    Chapter 4 The Phragmén-Lindelöf Theorem
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    Chapter 5 The Poisson Sum Formula and Applications
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    Chapter 6 The Riemann ζ-function
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    Chapter 7 About the Prime-number Theorem and the Zeros of the ζ-function
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    Chapter 8 The Eisenstein Series
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    Chapter 9 The Transformation of log η(τ) and the Theory of the Dedekind Sums
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    Chapter 10 The ϑ-functions
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    Chapter 11 Elliptic Functions and their Applications to Number Theory
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    Chapter 12 Formal Power Series and the Theory of Partitions
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    Chapter 13 Ramanujan’s Congruences and Identities
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    Chapter 14 Analytic Theory of Partitions
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    Chapter 15 Application of the Circle Method to Modular Forms of Positive Dimension
Attention for Chapter 8: The Eisenstein Series
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