: Gennady I. Arkhipov, Vladimir N. Chubarikov, Anatoly A. Karatsuba
: Trigonometric Sums in Number Theory and Analysis
: Walter de Gruyter GmbH& Co.KG
: 9783110197983
: De Gruyter Expositions in MathematicsISSN
: 1
: CHF 256.20
:
: Allgemeines, Lexika
: English
: 564
: Wasserzeichen/DRM
: PC/MAC/eReader/Tablet
: PDF

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.


Dr. Gennady I. ArkhipovandDr. 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.

Frontmatter1
Contents9
Introduction11
Chapter 1. Trigonometric integrals16
Chapter 2. Rational trigonometric sums58
Chapter 3. Weyl sums89
Chapter 4. Mean value theorems for multiple trigonometric sums154
Chapter 5. Estimates for multiple trigonometric sums191
Chapter 6. Several applications220
Chapter 7. Special cases of the theory of multiple trigonometric sums245
Chapter 8. The Hilbert–Kamke problem and its generalizations326
Chapter 9. The p-adic method in three problems of number theory371
Chapter 10. Estimates of multiple trigonometric sums with prime numbers422
Chapter 11. Some applications of trigonometric sums and integrals479
Chapter 12. Short Kloosterman sums492
Backmatter547