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

Korobov, N. M.

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.

Reviewer: E.Krätzel (Jena)

MSC:

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.

Keywords:

complete trigonometric sums; Weyl sums; distribution of fractional parts; normal numbers; quadrature formulas; Gauss sums; rational trigonometric sums; systems of congruences; numerical integration; interpolation; applications of trigonometric sums to numerical analysis

Citations:

Zbl 0229.10020; Zbl 0665.10026