Let K be a finite Galois extension of the field ℚ of rational numbers. We prove an asymptotic formula for the number of Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincides with any given conjugacy class in the Galois group of K/ℚ. In particular, this shows that there are infinitely many Piatetski-Shapiro primes of the form a² + nb² for any given natural number n.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-1,
author = {Y\i ld\i r\i m Akbal and Ahmet Muhtar G\"ulo\u glu},
title = {Piatetski-Shapiro meets Chebotarev},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {301-325},
zbl = {1317.11081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-1}
}
Yıldırım Akbal; Ahmet Muhtar Güloğlu. Piatetski-Shapiro meets Chebotarev. Acta Arithmetica, Tome 168 (2015) pp. 301-325. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-4-1/