科研之友
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摘要
Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with 1 <= a <= q - 1, it is clear that there exists one and only one b with 0 <= b <= q - 1 such that ab c (mod q). LetN(c, q) denotes the number of all solutions of the congruence equation ab c (mod q) for 1 <= a, b <= q - 1 in which a and (b) over bar are of opposite parity, where (b) over bar is defined by the congruence equation b (b) over bar 1(modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving (N(c, q) - 1/2 phi(q)) and Ramanujan's sum, and give two exact computational formulae.
- 出版日期2012-1
- 单位西北大学
