Trigonometric Sums in Number Theory and Analysis.
Title:
Trigonometric Sums in Number Theory and Analysis.
Author:
Arkhipov, Gennady I.
ISBN:
9783110197983
Personal Author:
Physical Description:
1 online resource (564 pages)
Series:
De Gruyter Expositions in Mathematics ; v.39
De Gruyter Expositions in Mathematics
Contents:
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.
Abstract:
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. Vinogradovś 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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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