Short notes

A generalization of the Gauss sum

H. M. Saliba, V. N. Chubarikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For the generalized Gauss sum
$$ S(N;a,q)=\sum\limits_{k=1}^{Nq} e\bigg(\frac1N \Big( k-\frac{a}{q}\Big)^2\bigg), $$
where $N,q$ are natural numbers, $a$ is integer, $0\leq a<q$, $(a,q)=1$, its value is determined.

Key words: Gauss sum, Poisson summation.

UDC: 511

Received: 26.09.2008

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