We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give necessary conditions for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-2-1,
author = {Hershy Kisilevsky and Michael O. Rubinstein},
title = {Chebotarev sets},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {97-124},
zbl = {1331.11082},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-2-1}
}
Hershy Kisilevsky; Michael O. Rubinstein. Chebotarev sets. Acta Arithmetica, Tome 168 (2015) pp. 97-124. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa171-2-1/