Number Theory

Table of Contents

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   Book Overview
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   Chapter 1 A Centennial History of the Prime Number Theorem
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   Chapter 2 Non-homogeneous Problems: Conjectures of Minkowski and Watson
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   Chapter 3 On the Oscillation Theorems of Pringsheim and Landau
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   Chapter 4 Modular Equations in Ramanujan’s Lost Notebook
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   Chapter 5 The abc-conjecture
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   Chapter 6 On Values of Linear and Quadratic Forms at Integral Points
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   Chapter 7 Variants of the Second Borel-Cantelli Lemma and their Applications in Metric Number Theory
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   Chapter 8 Pythagorean Triples
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    Chapter 9 Integer Points in Plane Regions and Exponential Sums
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    Chapter 10 Artin’s Conjecture for Polynomials Over Finite Fields
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    Chapter 11 Continuous Homomorphisms as Arithmetical Functions, and Sets of Uniqueness
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    Chapter 12 Hamburger’s Theorem on ζ(s) and the Abundance Principle for Dirichlet Series with Functional Equations
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    Chapter 13 A Survey of Number Theory and Cryptography
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    Chapter 14 Recent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions
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    Chapter 15 Algebraic Curves Over Finite Fields with many Rational Points and their Applications
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    Chapter 16 A Report on Artin’s Holomorphy Conjecture
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    Chapter 17 Siegel’s Main Theorem for Quadratic Forms
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    Chapter 18 Pfister’s Work on Sums of Squares
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    Chapter 19 Notes on the Prime Number Theorem-I
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    Chapter 20 Sums of Squares: An Elementary Method
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    Chapter 21 Solution of the Basic Problems of Discrete Geometry on the Plane
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    Chapter 22 Exponential Diophantine Equations Involving Products of Consecutive Integers and Related Equations
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    Chapter 23 Algebraic Independence of Transcendental Numbers: A Survey