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Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples.
The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects.
List of contents
Positive Finiteness of Number Systems.- On a Distribution Property of the Residual Order of a (mod p)- IV.- Diagonalizing "Bad" Hecke Operators on Spaces of Cusp Forms.- On the Hilbert-Kamke and the Vinogradov Problems in Additive Number Theory.- The Goldbach-Vinogradov Theorem in Arithmetic Progressions.- Densities of Sets of Primes Related to Decimal Expansion of Rational Numbers.- Spherical Functions on p-Adic Homogeneous Spaces.- On Modular forms of Weight (6n + 1)/5 Satisfying a Certain Differential Equation.- Some Aspects of the Modular Relation.- Zeros of Automorphic L-Functions and Noncyclic Base Change.- Analytic Properties of Multiple Zeta-Functions in Several Variables.- Cubic Fields and Mordell Curves.- Towards the Reciprocity of Quartic Theta-Weyl Sums, and Beyond.- Explicit Congruences for Euler Polynomials.- Square-Free Integers as Sums of Two Squares.- Some Applications of L-Functions to the Mean Value of the Dedekind Sums and Cochrane Sums.
Summary
Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory. Though the topics and descriptive details appear varied, they are unified by two underlying principles: first, making everything readable as a book, and second, making a smooth transition from traditional approaches to modern ones by providing a rich array of examples.
The chapters are presented in quite different in depth and cover a variety of descriptive details, but the underlying editorial principle enables the reader to have a unified glimpse of the developments of number theory. Thus, on the one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated. The book emphasizes a few common features such as functional equations for various zeta-functions, modular forms, congruence conditions, exponential sums, and algorithmic aspects.
