Akbal, Yıldırım2016-05-032016-05-032015-072015-0729-07-2015http://hdl.handle.net/11693/29039Cataloged from PDF version of thesis.Includes bibliographical references (leaves 39-40).Thesis (Ph. D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2015.Let K be a nite Galois extension of the eld 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 eld extensions, we conclude that there are in nitely many Piatetski-Shapiro primes lying in a given arithmetic progresion and furthermore there are in nitely many primes that can be expressed as a sum of a square and a xed positive integer multiple of another square.iv, 40 leaves : charts.Englishinfo:eu-repo/semantics/openAccessChebotarev density theoremPiatetski-Shapiro prime number theoremExponential sums over idealsThesisB150930