2005/05/05 by William D. Banks, Moubariz Z. Garaev, Banks, William D. +5
Mathematics · #11L07 #11N37 #11N60 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11L07 #msc:11N37 #msc:11N60
paper · pdf · doi:10.48550/arxiv.math/0505098
In the new version we use an idea of Moubariz Garaev (who is now a co-author) to improve some of the results of the previous version
openalex publication_date 2005/05/05 · arxiv created 2005/08/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We estimate exponential sums with the Fermat-like quotients fg(n) = \fracgn-1 - 1n \mand hg(n)=\fracgn-1-1P(n), where g and n are positive integers, n is composite, and P(n) is the largest prime factor of n. Clearly, both fg(n) and hg(n) are integers if n is a Fermat pseudoprime to base g, and if n is a Carmichael number this is true for all g coprime to n. Nevertheless, our bounds imply that the fractional parts \fg(n)\ and \hg(n)\ are uniformly distributed, on average over g for fg(n), and individually for hg(n). We also obtain similar results with the functions \widetilde fg(n) = gfg(n) and \widetilde hg(n) = ghg(n).