Exponential sums and their applications. Transl. from the Russian by Yu. N. Shakhov. (English) Zbl 0754.11022

Mathematics and Its Applications. Soviet Series. 80. Dordrecht etc.: Kluwer Academic Publishers. xv, 209 p. (1992).
This is a translation of the original Russian edition published by Nauka Moskva (1989; Zbl 0665.10026). It is a very nice introduction to the method of exponential sums. In general, the study of this method is very complicated. But in this monograph a sufficiently simple exposition of the fundamentals of the theory is given. Therefore, the book is suited for beginners in exponential sum theory. On the other hand it is of interest for specialists, because there are also some new results.


11L03 Trigonometric and exponential sums (general theory)
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11-02 Research exposition (monographs, survey articles) pertaining to number theory
65D32 Numerical quadrature and cubature formulas
11J71 Distribution modulo one
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.