Exponential Sums and their Applications

1992
ISBN: 978-0-7923-1647-3
Verlag: Springer Netherlands

Buch, Englisch, Band 80, 210 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1110 g

Reihe: Mathematics and its Applications

The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications. This volume presents an exposition of the fundamentals of the theory with the help of examples which show how exponential sums arise and how they are applied in problems of number theory and its applications.
The material is divided into three chapters which embrace the classical results of Gauss, and the methods of Weyl, Mordell and Vinogradov; the traditional applications of exponential sums to the distribution of fractional parts, the estimation of the Riemann zeta function; and the theory of congruences and Diophantine equations. Some new applications of exponential sums are also included.
It is assumed that the reader has a knowledge of the fundamentals of mathematical analysis and of elementary number theory.

Zielgruppe

Research

Autoren/Hrsg.

Korobov, N. M

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Complete Exponential Sums.- Weyl’s Sums.- Fractional Parts Distribution, Normal Numbers, and Quadrature Formulas.