On vanishing Fermat quotients and a bound of the Ihara sum
Number Theory
2011-04-21 v1
Abstract
We improve an estimate of A.Granville (1987) on the number of vanishing Fermat quotients modulo a prime when runs through primes . We use this bound to obtain an unconditional improvement of the conditional (under the Generalised Riemann Hypothesis) estimate of Y. Ihara (2006) on a certain sum, related to vanishing Fermat quotients. In turn this sum appears in the study of the index of certain subfields of of cyclotomic fields .
Keywords
Cite
@article{arxiv.1104.3910,
title = {On vanishing Fermat quotients and a bound of the Ihara sum},
author = {Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1104.3910},
year = {2011}
}