Open Access. Powered by Scholars. Published by Universities.®

Number Theory Commons

Open Access. Powered by Scholars. Published by Universities.®

208 Full-Text Articles 234 Authors 34,165 Downloads 57 Institutions

All Articles in Number Theory

Faceted Search

208 full-text articles. Page 2 of 8.

A Math Poem, Sara R. Katz 2017 Essex Street Academy

A Math Poem, Sara R. Katz

Journal of Humanistic Mathematics

No abstract provided.


Babylonian Numeration, Dominic Klyve 2017 Central Washington University

Babylonian Numeration, Dominic Klyve

Number Theory

No abstract provided.


Pascal's Triangle And Mathematical Induction, Jerry Lodder 2017 New Mexico State University

Pascal's Triangle And Mathematical Induction, Jerry Lodder

Number Theory

No abstract provided.


Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett 2017 Colorado State University-Pueblo

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

Number Theory

No abstract provided.


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

Primes, Divisibility, And Factoring, 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.


Construction Of The Figurate Numbers, Jerry Lodder 2017 New Mexico State University

Construction Of The Figurate Numbers, Jerry Lodder

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 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 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 ...


Algorithmic Factorization Of Polynomials Over Number Fields, Christian Schulz 2017 Rose-Hulman Institute of Technology

Algorithmic Factorization Of Polynomials Over Number Fields, Christian Schulz

Mathematical Sciences Technical Reports (MSTR)

The problem of exact polynomial factorization, in other words expressing a polynomial as a product of irreducible polynomials over some field, has applications in algebraic number theory. Although some algorithms for factorization over algebraic number fields are known, few are taught such general algorithms, as their use is mainly as part of the code of various computer algebra systems. This thesis provides a summary of one such algorithm, which the author has also fully implemented at https://github.com/Whirligig231/number-field-factorization, along with an analysis of the runtime of this algorithm. Let k be the product of the degrees of ...


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.


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.


Dynamical Systems And Zeta Functions Of Function Fields, Daniel Nichols 2017 University of Massachusetts Amherst

Dynamical Systems And Zeta Functions Of Function Fields, Daniel Nichols

Doctoral Dissertations

This doctoral dissertation concerns two problems in number theory. First, we examine a family of discrete dynamical systems in F_2[t] analogous to the 3x + 1 system on the positive integers. We prove a statistical result about the large-scale dynamics of these systems that is stronger than the analogous theorem in Z. We also investigate mx + 1 systems in rings of functions over a family of algebraic curves over F_2 and prove a similar result there.

Second, we describe some interesting properties of zeta functions of algebraic curves. Generally L-functions vanish only to the order required by their root number ...


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.


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.


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 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 ...


Digital Commons powered by bepress