Piatetski-Shapiro meets Chebotarev

• Autorzy: Yıldırım Akbal , Ahmet Muhtar Güloğlu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11B83: Special sequences and polynomials
• 11L07: Estimates on exponential sums
• 11R45: Density theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 4
• Strony: 301-325

Daty

wydano

2015

Twórcy

autor

Yıldırım Akbal

• Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey

autor

Ahmet Muhtar Güloğlu

• Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey

Identyfikatory

DOI

10.4064/aa167-4-1