Some heuristics and results for small cycles of the discrete logarithm-Reference-Cited by-同舟云学术

Some heuristics and results for small cycles of the discrete logarithm

Published:2005-06-28 Issue:253 Volume:75 Page:419-449
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Holden Joshua,Moree Pieter

Abstract

Brizolis asked the question: does every prime p p have a pair ( g , h ) (g,h) such that h h is a fixed point for the discrete logarithm with base g g ? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g g and h h . In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2006-75-253/S0025-5718-05-01768-0/S0025-5718-05-01768-0.pdf

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