Trigonometric Sums in Number Theory and Analysis (eBook)

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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 atthe Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University, Russia.

Frontmatter 1
Contents 9
Introduction 11
Chapter 1. Trigonometric integrals 16
Chapter 2. Rational trigonometric sums 58
Chapter 3. Weyl sums 89
Chapter 4. Mean value theorems for multiple trigonometric sums 154
Chapter 5. Estimates for multiple trigonometric sums 191
Chapter 6. Several applications 220
Chapter 7. Special cases of the theory of multiple trigonometric sums 245
Chapter 8. The Hilbert–Kamke problem and its generalizations 326
Chapter 9. The p-adic method in three problems of number theory 371
Chapter 10. Estimates of multiple trigonometric sums with prime numbers 422
Chapter 11. Some applications of trigonometric sums and integrals 479
Chapter 12. Short Kloosterman sums 492
Backmatter 547

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"The book is written very carefully and contains at the beginning of each chapter an introduction which is very well readable. It will certainly replace the former monographies on this theme."
J. Schoissengeier in: Monatshefte für Mathematik 1/2006

"The book will be useful for a wide range of mathematicians."
EMS newsletter 9/2005