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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.

MSC:
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