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Filtering by: Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics Committee Member Flahive, Mary Remove constraint Committee Member: Flahive, Mary

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Existence of Eta-Quotients for Squarefree Levels and Modular Type Supercongruences for Hypergeometric Functions

Creator:

Allen, Michael

Abstract:

In this dissertation, we consider two problems in number theory, both relating to modular forms. First we consider when a given modular form can be expressed as a quotient in Dedekind's $\eta$ function. Rouse and Webb \cite{RW} have determined the integers $N \leq 500$ such that the graded ring of...

Resource Type:

Dissertation
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
Overpartition Ranks, Cranks, and Frobenius Representations

Creator:

Morrill, Thomas

Abstract:

We generalize overpartition rank and crank generating functions to obtain k-fold variants, and give a combinatorial interpretation for each. The k-fold crank generating function is interpreted by extending the first and second residual cranks to a natural infinite family. The k-fold rank generating functions generate two families of buffered Frobenius...

Resource Type:

Dissertation
Subalgebras of the Split Octonions

Creator:

Bentz, Lida

Abstract:

We classify the subalgebras of the split octonions, paying particular attention to the null subalgebras and their extensions.

Resource Type:

Capstone Project
Continued fractions and the divisor at infinity on a hyperelliptic curve : examples and order bounds

Creator:

Daowsud, Katthaleeya

Abstract:

We use the theory of continued fractions over function fields in the setting of hyperelliptic curves of equation y²=f(x), with deg(f)=2g+2. By introducing a new sequence of polynomials defined in terms of the partial quotients of the continued fraction expansion of y, we are able to bound the sum of...

Resource Type:

Dissertation
Maximal operators along surfaces of revolution

Creator:

Le, Hung Viet

Abstract:

The study of differentiation of integrals has led to the study of maximal functions. In the development of harmonic analysis, the most powerful result connected with Lebesgue's theorem was that of the Hardy-Littlewood Maximal Theorem. This maximal theorem implies Lebesgue's theorem, and the maximal function and its variants have played...

Resource Type:

Dissertation
Asphericity of length 6 equations over torsion free groups

Creator:

Kim, Seong Kun

Resource Type:

Dissertation
Hilbert modular surfaces and uniformizing groups of Klein invariants

Creator:

Bell, Andrea Moreira

Resource Type:

Dissertation
Rigidity for a class of Coxeter groups

Creator:

Kaul, Anton

Resource Type:

Dissertation
Triangular billiards surfaces and translation covers

Creator:

Schmurr, Jason Peter

Abstract:

We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers.

Resource Type:

Dissertation

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Academic Affiliation

Mathematics[remove]10

Advisor

Bogley, William A.2
Schmidt, Thomas A.2
Chen, Lung Kee1
Dray, Tevian1
Petsche, Clayton J.1
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Commencement Year

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Current results range from 2000 to 2022

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Committee Member

Flahive, Mary[remove]10
Garity, Dennis3
Petsche, Clayton3
Escher, Christine2
Solmon, Donald2
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Creator

Allen, Michael1
Bell, Andrea Moreira1
Bentz, Lida1
Daowsud, Katthaleeya1
Kaul, Anton1
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Date

Date range begin – Date range end

Current results range from 2000 to 2022

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Decade

2020-20291
2010-20194
2000-20095

Degree Field

Mathematics10

Degree Level

Doctoral9
Master's1

Degree Name

Doctor of Philosophy (Ph.D.)9
Master of Science (M.S.)1

Language

English [eng]10

License

All rights reserved7
Attribution-ShareAlike 3.0 United States1

Non-Academic Affiliation

Oregon State University. Graduate School7

Peer Reviewed

No8

Resource Type

Dissertation9
Capstone Project1

Rights Statement

In Copyright8
Copyright Not Evaluated2

Subject

Curves, Algebraic2
Combinatorial group theory1
Continued fractions1
Coxeter complexes1
Differentiable dynamical systems1
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