TITLE

A note on the Lehmer problem over short intervals

AUTHOR(S)
Lu, Ya; Yi, Yuan
PUB. DATE
June 2011
SOURCE
Acta Mathematica Sinica;Jun2011, Vol. 27 Issue 6, p1115
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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 ∤ a + ā, where ā is an integer with 1 ≤ ā ≤ p − 1, aā ≡ c (mod p). It is well known that r( N, c; p) = 1/2 N + O( plog p). The main purpose of this paper is to give an asymptotic formula for Σ( r( N, c; p) − 1/2 N).
ACCESSION #
60368096

 

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