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. (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.
Reviewer: Matti Jutila (Turku)
MSC:
| 11L07 | Estimates on exponential sums |
| 11-02 | Research exposition (monographs, survey articles) pertaining to number theory |
| 11L03 | Trigonometric and exponential sums (general theory) |
| 11L40 | Estimates on character sums |
| 11P05 | Waring’s problem and variants |
| 11P55 | Applications of the Hardy-Littlewood method |
