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