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Three Topics in Analytic Number Theory.

BenlI, Kubra.

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Three Topics in Analytic Number Theory.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Three Topics in Analytic Number Theory./
Author:	BenlI, Kubra.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	90 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-03, Section: B.
Contained By:	Dissertations Abstracts International82-03B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28002472
ISBN:	9798672119175

Three Topics in Analytic Number Theory.
BenlI, Kubra.

Three Topics in Analytic Number Theory. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 90 p.

Source: Dissertations Abstracts International, Volume: 82-03, Section: B.

Thesis (Ph.D.)--University of Georgia, 2020.

This item must not be sold to any third party vendors.

This thesis discusses three topics in Number Theory, where the results are obtained by using analytic methods. First, we discuss results on the distribution of the small prime power residues modulo a prime. We give an elementary approach by using reciprocity laws first, and then we discuss how to improve and generalize these results using character sum estimates and sieve results. Secondly, we discuss a quantitative improvement on the number of weakly prime numbers, the primes that change to a composite number after altering a single digit. Finally, we discuss an asymptotic formula for the number of pure fields of fixed prime degree and bounded discriminant.

ISBN: 9798672119175Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Character sums

Three Topics in Analytic Number Theory.
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100 1 $a BenlI, Kubra. $0 (orcid)0000-0003-3567-4809 $3 3558920
245 1 0 $a Three Topics in Analytic Number Theory.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 90 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-03, Section: B.
500 $a Advisor: Pollack, Paul.
502 $a Thesis (Ph.D.)--University of Georgia, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis discusses three topics in Number Theory, where the results are obtained by using analytic methods. First, we discuss results on the distribution of the small prime power residues modulo a prime. We give an elementary approach by using reciprocity laws first, and then we discuss how to improve and generalize these results using character sum estimates and sieve results. Secondly, we discuss a quantitative improvement on the number of weakly prime numbers, the primes that change to a composite number after altering a single digit. Finally, we discuss an asymptotic formula for the number of pure fields of fixed prime degree and bounded discriminant.
590 $a School code: 0077.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Character sums
653 $a Partial covering of congruences
653 $a Prime numbers
653 $a Pure fields
653 $a Sieve methods
690 $a 0405
690 $a 0642
710 2 $a University of Georgia. $b Mathematics - PHD. $3 3558921
773 0 $t Dissertations Abstracts International $g 82-03B.
790 $a 0077
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28002472