On a Generalisation of a Lehmer Problem

Igor Shparlinski

Published 2006-07-18, updated 2006-07-19Version 2

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.