2021/07/19 by Sergeĭ Konyagin, Sergei Konyagin, Paul Pollack +2
Computer Science · Mathematics · Social Sciences · #Analytic Number Theory Research #Coding theory and cryptography #Historical Geopolitical and Social Dynamics #math.NT #msc:11A07 #msc:11A15 #msc:11N36
paper · pdf · doi:10.48550/arxiv.2107.08998
12 pages; accepted version incorporating minor edits
arxiv created 2021/08/31 · arxiv updated 2021/09/01
Write ordp(⋅) for the multiplicative order in \mathbbFp×. Recently, Matthew Just and the second author investigated the problem of classifying pairs α, β∈ ℚ×∖\± 1\ for which ordp(α) > ordp(β) holds for infinitely many primes p. They called such pairs order-dominant. We describe an easily-checkable sufficient condition for α,β to be order-dominant. Via the large sieve, we show that almost all integer pairs α,β satisfy our condition, with a power savings on the size of the exceptional set.