Trigonometric Sums in Number Theory and Analysis

1. Auflage 2004
ISBN: 978-3-11-016266-0
Verlag: De Gruyter

Buch, Englisch, 554 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 1124 g

Reihe: ISSN

The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov´s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.

Autoren/Hrsg.

Arkhipov, Gennady I.

Chubarikov, Vladimir N.

Karatsuba, Anatoly A.

Weitere Mitwirkende

Shishkova, Maria

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Frontmatter
Contents
Introduction
Chapter 1. Trigonometric integrals
Chapter 2. Rational trigonometric sums
Chapter 3. Weyl sums
Chapter 4. Mean value theorems for multiple trigonometric sums
Chapter 5. Estimates for multiple trigonometric sums
Chapter 6. Several applications
Chapter 7. Special cases of the theory of multiple trigonometric sums
Chapter 8. The Hilbert–Kamke problem and its generalizations
Chapter 9. The p-adic method in three problems of number theory
Chapter 10. Estimates of multiple trigonometric sums with prime numbers
Chapter 11. Some applications of trigonometric sums and integrals
Chapter 12. Short Kloosterman sums
Backmatter

Über Autor(innen)

Dr. Gennady I. Arkhipov and Dr. Anatoly A. Karatsuba are working at the Steklov Mathematical Institute of the Russian Academy of Sciences at Moscow, Russia. Vladimir N. Chubarikov is Professor at the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University, Russia.