On a Generalisation of a Lehmer Problem

2006/07/18 by Igor Shparlinski, Shparlinski, Igor
Mathematics · #11A07 #11K38 #11L40 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A07 #msc:11K38 #msc:11L40

paper · pdf · doi:10.48550/arxiv.math/0607414

17 pages

arxiv created 2006/07/19 · arxiv updated 2009/12/01

Abstract

We consider a generalisation of the classical Lehmer problem about the distribution of modular inverses in arithmetic progression, introduced by E. Alkan, F. Stan and A. Zaharescu. Using bounds of sums of multiplicative characters instead of traditionally applied to this kind of problem Kloosterman sums, we improve their results in several directions.

Related

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• Triple sums of Kloosterman sums and the discrepancy of modular inverses
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• Multiple Mertens theorems for arithmetic progressions