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Multiplicative and Additive Arithmetic Functions and Formal Power Series.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Multiplicative and Additive Arithmetic Functions and Formal Power Series./
Author:	Snell, John Byron.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	67 p.
Notes:	Source: Masters Abstracts International, Volume: 83-03.
Contained By:	Masters Abstracts International83-03.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28648404
ISBN:	9798538160082

Multiplicative and Additive Arithmetic Functions and Formal Power Series.
Snell, John Byron.

Multiplicative and Additive Arithmetic Functions and Formal Power Series. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 67 p.

Source: Masters Abstracts International, Volume: 83-03.

Thesis (M.S.)--The University of Texas at El Paso, 2021.

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

The theory of arithmetic functions and the theory of formal power series are classical and active parts of mathematics. Algebraic operations on sets of arithmetic functions, called convolutions, have an important place in the theory of arithmetic functions. The theory of formal power series also has its place firmly anchored in abstract algebra.A first goal of this thesis will be to present a parallelism of known characterizations of the concepts of multiplicative and additive for arithmetic functions (Theorems 2.1.2 and 2.2.3) on the one hand and for formal power series on the other (Theorems 3.4.3 and 3.4.4). Therefore, in Chapter 1 and in the first part of Chapter 3 are listed notions and properties that make possible the transposition from arithmetic functions to formal power series. Further, an approach in which formal power series brought to the fore (Sections 3.1 and 3.2) will add new elements in our study on multiplicative arithmetic functions (Section 3.3). So, if mainly, our presentation of Section 3.3 follows P.J. McCarthy's book [6], the proofs of some main results on completely and specially multiplicative functions has been replaced with new proofs (Theorems 3.2.6, 3.2.7, 3.3.3, 3.3.4) using Bell series. This was a second goal of giving new proofs using Bell series, and so we bring the two topics (arithmetic functions and formal power series) closer together. If in the achievement of the first goal a significant role was played by the embedding of the ring of formal power series in the unitary ring of arithmetic functions, in the case of the second goal, Theorem 2.24 and 2.25 of T.M. Apostol's book [1] influenced me to use the Bell series in proofs.

ISBN: 9798538160082Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Multiplicative

Multiplicative and Additive Arithmetic Functions and Formal Power Series.
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245 1 0 $a Multiplicative and Additive Arithmetic Functions and Formal Power Series.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 67 p.
500 $a Source: Masters Abstracts International, Volume: 83-03.
500 $a Advisor: Schwab, Emil Daniel.
502 $a Thesis (M.S.)--The University of Texas at El Paso, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a The theory of arithmetic functions and the theory of formal power series are classical and active parts of mathematics. Algebraic operations on sets of arithmetic functions, called convolutions, have an important place in the theory of arithmetic functions. The theory of formal power series also has its place firmly anchored in abstract algebra.A first goal of this thesis will be to present a parallelism of known characterizations of the concepts of multiplicative and additive for arithmetic functions (Theorems 2.1.2 and 2.2.3) on the one hand and for formal power series on the other (Theorems 3.4.3 and 3.4.4). Therefore, in Chapter 1 and in the first part of Chapter 3 are listed notions and properties that make possible the transposition from arithmetic functions to formal power series. Further, an approach in which formal power series brought to the fore (Sections 3.1 and 3.2) will add new elements in our study on multiplicative arithmetic functions (Section 3.3). So, if mainly, our presentation of Section 3.3 follows P.J. McCarthy's book [6], the proofs of some main results on completely and specially multiplicative functions has been replaced with new proofs (Theorems 3.2.6, 3.2.7, 3.3.3, 3.3.4) using Bell series. This was a second goal of giving new proofs using Bell series, and so we bring the two topics (arithmetic functions and formal power series) closer together. If in the achievement of the first goal a significant role was played by the embedding of the ring of formal power series in the unitary ring of arithmetic functions, in the case of the second goal, Theorem 2.24 and 2.25 of T.M. Apostol's book [1] influenced me to use the Bell series in proofs.
590 $a School code: 0459.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Multiplicative
653 $a Additive
653 $a Arithmetic functions
653 $a Formal power series
690 $a 0405
690 $a 0642
710 2 $a The University of Texas at El Paso. $b Mathematical Sciences. $3 1022837
773 0 $t Masters Abstracts International $g 83-03.
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791 $a M.S.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28648404