A note on the Lehmer problem over short intervals

作者：Lu, Ya Ming^*; Yi, Yuan

来源：Acta Mathematica Sinica-English Series, 2011, 27(6): 1115-1120.

DOI：10.1007/s10114-011-8554-8

• Lehmer problem
• character sum
• Dirichlet L-function

Let p be an odd prime, c be an integer with (c, p) = 1, and let N be a positive integer with N <= p - 1. Denote by r(N, c; p) the number of integers a satisfying 1 <= a <= N and 2 vertical bar a + A, where A is an integer with 1 <= A <= p - 1, aA equivalent to c (mod p). It is well known that r(N, c; p) = 1/2N + O(p (1/2)log(2) p). The main purpose of this paper is to give an asymptotic formula for Sigma (c=1) (p-1) (r(N, c; p) - 1/2N)(2).

• 出版日期2011-6
• 单位西安交通大学