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Filtering by: Subject Algebraic number theory Remove constraint Subject: Algebraic number theory

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Sums of subsets of certain algebraic systems

Creator:

Higdem, Roger Leon

Abstract:

In this thesis we investigate the extension of certain theorems of additive number theory to three algebraic systems. A generalization of a theorem by Cauchy and Davenport on the cardinality of the sum of two sets of residue classes is given. We obtain and compare estimates for the order of...

Resource Type:

Dissertation
A construction of the real numbers using nested closed intervals

Creator:

Huang, Nancy Mang-ze

Abstract:

It is well- known that a real number can be defined as an equivalence class of fundamental rational sequences. In fact, it is also possible to define a real number as an equivalence class of sequences of nested closed rational intervals. This paper is devoted to the latter case.

Resource Type:

Masters Thesis

Full Text:

number can be defined as an equiva- lence class of fundamental rational sequences. In fact, it is also
Modulo m properties of the Fibonacci sequence

Creator:

Vinson, John Ellsworth

Resource Type:

Masters Thesis

Full Text:

2 positive integers, that is, a number theoretic function. We now define another number theoretic
On Small Heights of Totally p-adic Numbers

Creator:

Stacy, Emerald T.

Abstract:

The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height...

Resource Type:

Dissertation

Full Text:

, Galois theory, and the theory of algebraic number fields. We review the basic definitions of absolute
An inequality for the number of integers in the sum of two sets of integers

Creator:

Lim, Yeam Seng

Resource Type:

Masters Thesis

Full Text:

An inequality for the number of integers in the sum of two
Proofs and comparisons of the Mann-Dyson estimation theorems

Creator:

Bregel, Maurice Leonard

Abstract:

Let A and B be two subsets of the set of all non-negative integers with 0 ε A and O ε B. The sum of the sets A and B is the set C = A + B = {a + b: a ε A, b ε B). For n...

Resource Type:

Masters Thesis

Full Text:

) . These lower bounds are consequences of well known theorems from additive number theory. The word
Khinchin's theorem on the Schnirelmann density of sums of sets of integers

Creator:

Gregersen, Gordon Stanley

Abstract:

In 1932 A. Ya. Khinchin gave the first partial solution of the celebrated 1931 αβ Conjecture of L.G. Schnirelmann and E. Landau of the density of sums of sets on integers, which was completely proved in 1942 by H.B. Mann. Khinchin's theorem is proved along with theorems of P. Scherk...

Resource Type:

Masters Thesis

Full Text:

) set of nonnegative integers and let A(n) be the number of positive integers of A which do not exceed
Gaussian integer analogues of two theorems of Mann for positive integers

Creator:

Morgali, Ronald Ralph

Resource Type:

Masters Thesis

Full Text:

|aeA, beB}. For n > 0 we denote the number of positive integers in the set C which do not exceed n by
New theorems and examples for Freedman's density spaces

Creator:

Olson, Arthur Eugene, Jr

Resource Type:

Masters Thesis

Full Text:

Numbers 21 3. 4 Some s -sets Generated by Other Subsets of the Positive Real Number 29 3. 5 Other
Some conditions for a given positive integer to be contained in a sum of sets of nonnegative integers

Creator:

Pierce, Patricia Carrie

Abstract:

In this thesis, we study conditions not involving density which guarantee that a given positive integer is contained in a sum of sets of nonnegative integers. We survey the literature, give more detailed proofs of some known theorems, develop some new theorems, and make some conjectures.

Resource Type:

Masters Thesis

Full Text:

positive integer, A(n) denotes the number of positive integers not greater than n. k In this thesis we

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Academic Affiliation

Mathematics23

Advisor

Stalley, Robert D.9
Stalley, R. D.4
Arnold, B. H.2
Flahive, Mary E.1
Petsche, Clayton1
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Commencement Year

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Current results range from 1952 to 2023

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Guo, Ren2
Dascaliuc, Radu1
Finch, David1
Finch, David V.1
Flahive, Mary1
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Creator

Bregel, Maurice Leonard1
Brown, Robert Wallace1
Daily, Mary Lou1
Damewood, Leroy Mitchell1
Dietel, Brian Christopher1
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Current results range from 1952 to 2023

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2020-20291
2010-20192
2000-20092
1980-19891
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1960-196912
1950-19591

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Mathematics23

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Master's12
Doctoral11

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Doctor of Philosophy (Ph.D.)11
Master of Science (M.S.)9
Master of Arts (M.A.)3

Language

English [eng]23

License

All rights reserved4

Non-Academic Affiliation

Oregon State University. Graduate School20

Peer Reviewed

No22

Resource Type

Masters Thesis12
Dissertation11

Rights Statement

Copyright Not Evaluated17
In Copyright6

Subject

Number theory18
Galois theory2
Algebra, Boolean1
Algebraic fields1
Algebraic number theory1
more Subjects »

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