New Conjectures and Results for Small Cycles of the Discrete Logarithm
| dc.creator | Holden, Joshua | |
| dc.creator | Moree, Pieter | |
| dc.date | 2003-05-21 | |
| dc.date | 2003-06-04 | |
| dc.date.accessioned | 2026-07-07T04:58:10Z | |
| dc.date.available | 2026-07-07T04:58:10Z | |
| dc.description | Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base 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 $g$ and $h$. In this paper we give a summary of conjectures and results which follow from these heuristics, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results. | |
| dc.description | 10 pages, to appear in the proceedings of the "Conference in Number Theory in Honour of Professor H.C. Williams", 2003. Version 2: Fixed typo in Theorem 1 (missing exponent) | |
| dc.identifier | https://arxiv.org/abs/math/0305305 | |
| dc.identifier | http://arxiv.org/abs/math/0305305 | |
| dc.identifier | In High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, AMS, 2004, pp. 245--254. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67531 | |
| dc.subject | Number Theory | |
| dc.title | New Conjectures and Results for Small Cycles of the Discrete Logarithm | |
| dc.type | text |