Some new sums related to D. H. Lehmer problem
Han Zhang, Wenpeng Zhang (2015)
Czechoslovak Mathematical Journal
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About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let be a prime, and let denote the number of all such that and . The main purpose of this paper is using the analytic method, the estimate for character sums and trigonometric sums to study the asymptotic properties of the counting function and give an interesting asymptotic formula...