# Trigonometric sum

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A finite sum of the form where is an integer and is a real-valued function of . More general sums of the following form are also called trigonometric sums: where is a real-valued function and is an arbitrary complex-valued function.

If is a polynomial, then is called a Weyl sum; if the polynomial has rational coefficients, then is called a rational trigonometric sum; if , then is called a complete trigonometric sum; if and when is a prime number while when is a composite number, then is called a trigonometric sum over prime numbers; if , and is a polynomial, then is called a multiple Weyl sum. A basic problem in the theory of trigonometric sums is that of finding upper bounds for the moduli of and .

How to Cite This Entry:
Trigonometric sum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Trigonometric_sum&oldid=15501
This article was adapted from an original article by A.A. Karatsuba (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article