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Primes, Divisibility, And Factoring, Dominic Klyve 2017 Central Washington University

Primes, Divisibility, And Factoring, Dominic Klyve

Number Theory

No abstract provided.


Babylonian Numeration, Dominic Klyve 2017 Central Washington University

Babylonian Numeration, Dominic Klyve

Number Theory

No abstract provided.


Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett 2017 Colorado State University-Pueblo

Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett

Number Theory

No abstract provided.


Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther 2017 The Graduate Center, City University of New York

Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

This thesis comes in four parts, which can be read independently of each other.

In the first chapter, we prove a generalization of Poonen's finite field Bertini theorem, and use this to show that the obvious obstruction to embedding a curve in some smooth surface is the only obstruction over perfect fields, extending a result of Altman and Kleiman. We also prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.

In the second chapter, for a fixed base curve over a finite field of characteristic at least 5 ...


Diophantine Approximation And The Atypical Numbers Of Nathanson And O'Bryant, David Seff 2017 The Graduate Center, City University of New York

Diophantine Approximation And The Atypical Numbers Of Nathanson And O'Bryant, David Seff

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

For any positive real number $\theta > 1$, and any natural number $n$, it is obvious that sequence $\theta^{1/n}$ goes to 1. Nathanson and O'Bryant studied the details of this convergence and discovered some truly amazing properties. One critical discovery is that for almost all $n$, $\displaystyle\floor{\frac{1}{\fp{\theta^{1/n}}}}$ is equal to $\displaystyle\floor{\frac{n}{\log\theta}-\frac{1}{2}}$, the exceptions, when $n > \log_2 \theta$, being termed atypical $n$ (the set of which for fixed $\theta$ being named $\mcA_\theta$), and that for $\log\theta$ rational, the number of atypical $n ...


From Simplest Recursion To The Recursion Of Generalizations Of Cross Polytope Numbers, Yutong Yang 2017 Kennesaw State University

From Simplest Recursion To The Recursion Of Generalizations Of Cross Polytope Numbers, Yutong Yang

Honors College Capstones and Theses

My research project involves investigations in the mathematical field of combinatorics. The research study will be based on the results of Professors Steven Edwards and William Griffiths, who recently found a new formula for the cross-polytope numbers. My topic will be focused on "Generalizations of cross-polytope numbers". It will include the proofs of the combinatorics results in Dr. Edwards and Dr. Griffiths' recently published paper. $E(n,m)$ and $O(n,m)$, the even terms and odd terms for Dr. Edward's original combinatorial expression, are two distinct combinatorial expressions that are in fact equal. But there is no obvious ...


Roman Domination In Complementary Prisms, Alawi I. Alhashim 2017 East Tennessee State University

Roman Domination In Complementary Prisms, Alawi I. Alhashim

Electronic Theses and Dissertations

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number ...


On The Reality Of Mathematics, Brendan Ortmann 2017 Southeastern University - Lakeland

On The Reality Of Mathematics, Brendan Ortmann

Selected Student Publications

Mathematics is an integral cornerstone of science and society at large, and its implications and derivations should be considered. That mathematics is frequently abstracted from reality is a notion not countered, but one must also think upon its physical basis as well. By segmenting mathematics into its different, abstract philosophies and real-world applications, this paper seeks to peer into the space that mathematics seems to fill; that is, to understand how and why it works. Under mathematical theory, Platonism, Nominalism, and Fictionalism are analyzed for their validity and their shortcomings, in addition to the evaluation of infinities and infinitesimals, to ...


On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi 2017 The University of Western Ontario

On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi

Electronic Thesis and Dissertation Repository

The objective of the study is to investigate the behaviour of the inner products of vector-valued Poincare series, for large weight, associated to submanifolds of a quotient of the complex unit ball and how vector-valued automorphic forms could be constructed via Poincare series. In addition, it provides a proof of that vector-valued Poincare series on an irreducible bounded symmetric domain span the space of vector-valued automorphic forms.


Rainbow Arithmetic Progressions, Steve Butler, Craig Erickson, Leslie Hogben, Kirsten Hogenson, Lucas Kramer, Richard Kramer, Jephian C. H. Lin, Ryan R. Martin, Derrick Stolee, Nathan Warnberg, Michael Young 2017 Iowa State University

Rainbow Arithmetic Progressions, Steve Butler, Craig Erickson, Leslie Hogben, Kirsten Hogenson, Lucas Kramer, Richard Kramer, Jephian C. H. Lin, Ryan R. Martin, Derrick Stolee, Nathan Warnberg, Michael Young

Leslie Hogben

In this paper, we investigate the anti-Ramsey (more precisely, anti-van der Waerden) properties of arithmetic progressions. For positive integers n and k, the expression aw([n]; k) denotes the smallest number of colors with which the integers f1; : : : ; ng can be colored and still guarantee there is a rainbow arithmetic progression of length k. We establish that aw([n]; 3) = (log n) and aw([n]; k) = n1o(1) for k 4. For positive integers n and k, the expression aw(Zn; k) denotes the smallest number of colors with which elements of the cyclic group of order n can be ...


Scaling Of Spectra Of Cantor-Type Measures And Some Number Theoretic Considerations, Isabelle Kraus 2017 University of Central Florida

Scaling Of Spectra Of Cantor-Type Measures And Some Number Theoretic Considerations, Isabelle Kraus

Honors in the Major Theses

We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore ways to determine when an odd natural number m generates a complete or incomplete Fourier basis for a Cantor-type measure with scale g.


On P-Adic Fields And P-Groups, Luis A. Sordo Vieira 2017 University of Kentucky

On P-Adic Fields And P-Groups, Luis A. Sordo Vieira

Theses and Dissertations--Mathematics

The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to ...


Combinatorics Of Compositions, Meghann M. Gibson 2017 Georgia Southern University

Combinatorics Of Compositions, Meghann M. Gibson

Electronic Theses & Dissertations

Integer compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.


Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson 2016 University of Tennessee, Knoxville

Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson

Masters Theses

This study has been written to illustrate the development from early mathematical learning (grades 3-8) to secondary education regarding the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. It investigates the progression of the mathematics presented to the students by the current curriculum adopted by the Rhea County School System and the mathematics academic standards set forth by the State of Tennessee.


On The Free And G-Saturated Weight Monoids Of Smooth Affine Spherical Varieties For G=Sl(N), Won Geun Kim 2016 The Graduate Center, City University of New York

On The Free And G-Saturated Weight Monoids Of Smooth Affine Spherical Varieties For G=Sl(N), Won Geun Kim

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

Let $X$ be an affine algebraic variety over $\mathbb{C}$ equipped with an action of a connected reductive group $G$. The weight monoid $\Gamma(X)$ of $X$ is the set of isomorphism classes of irreducible representations of $G$ that occur in the coordinate ring $\mathbb{C}[X]$ of $X$. Losev has shown that if $X$ is a smooth affine spherical variety, that is, if $X$ is smooth and $\mathbb{C}[X]$ is multiplicity-free as a representation of $G$, then $\Gamma(X)$ determines $X$ up to equivariant automorphism.

Pezzini and Van Steirteghem have recently obtained a combinatorial characterization of the weight ...


Explicit Formulae And Trace Formulae, Tian An Wong 2016 The Graduate Center, City University of New York

Explicit Formulae And Trace Formulae, Tian An Wong

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

In this thesis, motivated by an observation of D. Hejhal, we show that the explicit formulae of A. Weil for sums over zeroes of Hecke L-functions, via the Maass-Selberg relation, occur in the continuous spectral terms in the Selberg trace formula over various number fields. In Part I, we discuss the relevant parts of the trace formulae classically and adelically, developing the necessary representation theoretic background. In Part II, we show how show the explicit formulae intervene, using the classical formulation of Weil; then we recast this in terms of Weil distributions and the adelic formulation of Weil. As an ...


P-Adic L-Functions And The Geometry Of Hida Families, Joseph Kramer-Miller 2016 Graduate Center, City University of New York

P-Adic L-Functions And The Geometry Of Hida Families, Joseph Kramer-Miller

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects


A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L ...


Comparing Local Constants Of Ordinary Elliptic Curves In Dihedral Extensions, Sunil Chetty 2016 College of Saint Benedict/Saint John's University

Comparing Local Constants Of Ordinary Elliptic Curves In Dihedral Extensions, Sunil Chetty

Mathematics Faculty Publications

We establish, for a substantial class of elliptic curves, that the arithmetic local constants introduced by Mazur and Rubin agree with quotients of analytic root numbers.


The Evolution Of Cryptology, Gwendolyn Rae Souza 2016 California State University - San Bernardino

The Evolution Of Cryptology, Gwendolyn Rae Souza

Electronic Theses, Projects, and Dissertations

We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of ...


Mathematical Reasoning And The Inductive Process: An Examination Of The Law Of Quadratic Reciprocity, Nitish Mittal 2016 California State University - San Bernardino

Mathematical Reasoning And The Inductive Process: An Examination Of The Law Of Quadratic Reciprocity, Nitish Mittal

Electronic Theses, Projects, and Dissertations

This project investigates the development of four different proofs of the law of quadratic reciprocity, in order to study the critical reasoning process that drives discovery in mathematics. We begin with an examination of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric simplification of Gauss’ third proof. Finally, we finish with an examination of one of the modern proofs of this theorem published in 1991 by Rousseau. Through this investigation we aim to analyze the different strategies used ...


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