Number Theory

Front Matter....Pages i-vii
A Centennial History of the Prime Number Theorem....Pages 1-14
Non-homogeneous Problems: Conjectures of Minkowski and Watson....Pages 15-41
On the Oscillation Theorems of Pringsheim and Landau....Pages 43-54
Modular Equations in Ramanujan’s Lost Notebook....Pages 55-74
The abc-conjecture....Pages 75-105
On Values of Linear and Quadratic Forms at Integral Points....Pages 107-119
Variants of the Second Borel-Cantelli Lemma and their Applications in Metric Number Theory....Pages 121-140
Pythagorean Triples....Pages 141-155
Integer Points in Plane Regions and Exponential Sums....Pages 157-166
Artin’s Conjecture for Polynomials Over Finite Fields....Pages 167-181
Continuous Homomorphisms as Arithmetical Functions, and Sets of Uniqueness....Pages 183-200
Hamburger’s Theorem on ζ(s) and the Abundance Principle for Dirichlet Series with Functional Equations....Pages 201-216
A Survey of Number Theory and Cryptography....Pages 217-239
Recent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions....Pages 241-286
Algebraic Curves Over Finite Fields with many Rational Points and their Applications....Pages 287-300
A Report on Artin’s Holomorphy Conjecture....Pages 301-314
Siegel’s Main Theorem for Quadratic Forms....Pages 315-324
Pfister’s Work on Sums of Squares....Pages 325-349
Notes on the Prime Number Theorem-I....Pages 351-370
Sums of Squares: An Elementary Method....Pages 371-399
Solution of the Basic Problems of Discrete Geometry on the Plane....Pages 401-461
Exponential Diophantine Equations Involving Products of Consecutive Integers and Related Equations....Pages 463-495
Algebraic Independence of Transcendental Numbers: A Survey....Pages 497-527