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On Some Problems Concerning Integer Recurring Sequences.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On Some Problems Concerning Integer Recurring Sequences./
Author:	Agrawal, Komal.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
Description:	106 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
Contained By:	Dissertations Abstracts International83-12B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29061920
ISBN:	9798834004318

On Some Problems Concerning Integer Recurring Sequences.
Agrawal, Komal.

On Some Problems Concerning Integer Recurring Sequences. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 106 p.

Source: Dissertations Abstracts International, Volume: 83-12, Section: B.

Thesis (Ph.D.)--University of Georgia, 2022.

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

This thesis focuses on the arithmetic of certain recurring sequences. We consider the sequences an-1 , the Fibonacci sequence, and more general Lucas sequence. The first section is inspired by Artin's primitive root conjecture. We prove that if a,b are multiplicatively independent, then for almost all prime numbers p , one of a,b,ab, a2b, ab2 has order exceeding p 8/15 + epsilon(p) . We also show that for infinitely many primes p , the order of the Fibonacci Sequence is as large as possible. In the second section we prove the existence and continuity of the distribution functions of the density of normal and primitive elements in a finite field and the reciprocal sum of divisors of Lucas sequences.

ISBN: 9798834004318Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Interger recurring sequences

On Some Problems Concerning Integer Recurring Sequences.
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100 1 $a Agrawal, Komal. $3 3692495
245 1 0 $a On Some Problems Concerning Integer Recurring Sequences.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2022
300 $a 106 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
500 $a Advisor: Pollack, Paul.
502 $a Thesis (Ph.D.)--University of Georgia, 2022.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis focuses on the arithmetic of certain recurring sequences. We consider the sequences an-1 , the Fibonacci sequence, and more general Lucas sequence. The first section is inspired by Artin's primitive root conjecture. We prove that if a,b are multiplicatively independent, then for almost all prime numbers p , one of a,b,ab, a2b, ab2 has order exceeding p 8/15 + epsilon(p) . We also show that for infinitely many primes p , the order of the Fibonacci Sequence is as large as possible. In the second section we prove the existence and continuity of the distribution functions of the density of normal and primitive elements in a finite field and the reciprocal sum of divisors of Lucas sequences.
590 $a School code: 0077.
650 4 $a Mathematics. $3 515831
653 $a Interger recurring sequences
653 $a Fibonacci sequence
653 $a Lucas sequence
690 $a 0405
710 2 $a University of Georgia. $b Mathematics - PHD. $3 3558921
773 0 $t Dissertations Abstracts International $g 83-12B.
790 $a 0077
791 $a Ph.D.
792 $a 2022
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29061920