We prove an upper bound for the number of primes p ≤ x in an arithmetic progression 1 (mod Q) that are exceptional in the sense that has no generator in the interval [1,B]. As a consequence we prove that if with a sufficiently large absolute constant c, then there exists a prime q dividing Q such that for some positive integer b ≤ B. Moreover we estimate the number of such q’s under suitable conditions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-5,
author = {Jacek Pomyka\l a},
title = {On q-orders in primitive modular groups},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {397-404},
zbl = {1320.11101},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-5}
}
Jacek Pomykała. On q-orders in primitive modular groups. Acta Arithmetica, Tome 166 (2014) pp. 397-404. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-5/