Piatetski-Shapiro meets Chebotarev

Yıldırım Akbal, and Ahmet Muhtar Güloğlu. "Piatetski-Shapiro meets Chebotarev." Acta Arithmetica 167.4 (2015): 301-325. <http://eudml.org/doc/278969>.

@article{YıldırımAkbal2015,
abstract = {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.},
author = {Yıldırım Akbal, Ahmet Muhtar Güloğlu},
journal = {Acta Arithmetica},
keywords = {Chebotarev's density theorem; Piatetski-Shapiro prime number theorem; exponential sums over ideals; generalized Vaughan's identity; van der Corput's method; Vinogradov's method},
language = {eng},
number = {4},
pages = {301-325},
title = {Piatetski-Shapiro meets Chebotarev},
url = {http://eudml.org/doc/278969},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Yıldırım Akbal
AU - Ahmet Muhtar Güloğlu
TI - Piatetski-Shapiro meets Chebotarev
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 4
SP - 301
EP - 325
AB - 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.
LA - eng
KW - Chebotarev's density theorem; Piatetski-Shapiro prime number theorem; exponential sums over ideals; generalized Vaughan's identity; van der Corput's method; Vinogradov's method
UR - http://eudml.org/doc/278969
ER -