Piatetski-shapir prime number theorem and chebotarev density theorem
Date
2015-07
Authors
Editor(s)
Advisor
Güloğlu, Ahmet Muhtar
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Print ISSN
Electronic ISSN
Publisher
Volume
Issue
Pages
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
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.
Course
Other identifiers
Book Title
Degree Discipline
Mathematics
Degree Level
Doctoral
Degree Name
Ph.D. (Doctor of Philosophy)