Piatetski-Shapiro asal sayı teoremi ve Chebotarev yoğunluk teoremi

Let K be a finite Galois extension of the field Q of rational numbers. In this thesis, we derive an asymptotic formula for the number of the Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincide with any given conjugacy class in the Galois group of K=Q. Applying this theorem to appropriate field extensions, we conclude that there are infinitely many Piatetski-Shapiro primes lying in a given arithmetic progresion and furthermore there are infinitely many primes that can be expressed as a sum of a square and a fixed positive integer multiple of another square.