Geodesic
Piatetski-Shapiro meets Chebotarev
Yıldırım Akbal 1   ; Ahmet Muhtar Güloğlu 1
1 Department of Mathematics Bilkent University 06800 Bilkent, Ankara, Turkey
Acta Arithmetica, Tome 167 (2015) no. 4, pp. 301-325 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $K$ be a finite Galois extension of the field ${\mathbb Q}$ 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 $K/{\mathbb Q}$. In particular, this shows that there are infinitely many Piatetski-Shapiro primes of the form $a^2 + n b^2$ for any given natural number $n$.
DOI : 10.4064/aa167-4-1
Keywords: finite galois extension field mathbb rational numbers prove asymptotic formula number piatetski shapiro primes exceeding given quantity which associated frobenius class automorphisms coincides given conjugacy class galois group mathbb particular shows there infinitely many piatetski shapiro primes form given natural number

Yıldırım Akbal  1   ; Ahmet Muhtar Güloğlu  1

1 Department of Mathematics Bilkent University 06800 Bilkent, Ankara, Turkey 
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Yıldırım Akbal; Ahmet Muhtar Güloğlu. Piatetski-Shapiro meets Chebotarev. Acta Arithmetica, Tome 167 (2015) no. 4, pp. 301-325. doi: 10.4064/aa167-4-1

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