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Trigonometric sums in number theory and analysis. Transl. from the Russian. (English) Zbl 1074.11043
de Gruyter Expositions in Mathematics 39. Berlin: Walter de Gruyter; (ISBN 3-11-016266-0/hbk). x, 554 p. EUR 128.00; sFr. 205.00; $ 128.95 (2004).
The first nine chapters of this book constitute a translation of the Russian original [Theory of multiple trigonometric sums (1987; Zbl 0638.10037)]. In the present English edition, three chapters have been added: 10. Estimates of multiple trigonometric sums with prime numbers, 11. Some applications of trigonometric sums and integrals, 12. Short Kloosterman sums. These contain expositions of more recent research and results.

11L07Estimates on exponential sums
11-02Research monographs (number theory)
11L03Trigonometric and exponential sums, general
11L40Estimates on character sums
11P05Waring’s problem and variants
11P55Applications of the Hardy-Littlewood method