Research
I am interested in Analytic Number Theory. Particularly, my thesis focused on the arithmetic of certain recurring sequences like the $a^n-1$
sequence, the Fibonacci sequence, and more general Lucas sequence. The first section of my theis is inspired by Artin’s primitive root conjecture and proved that if $a,b$ are multiplicatively independent, then for almost all prime numbers $p$, one of $a,b,ab, a^2b, ab^2$ has order exceeding $p^{\frac{8}{15}+ \epsilon(p)}$. It also proved that for infinitely many primes $p$, the order of the Fibonacci Sequence is as large as possible.
In the second section I prove the existence and continuity of the distribution functions of the density of normal and primitive elements in a finite field and the reciprocal sum of divisors of Lucas sequences.
Publications
- Finite sets containing near-primitive roots (w/ P. Pollack)
J. Number Theory 225 (2021), 360–373
Talks
- On Some Problems Concerning Integer Recurring Sequences
Thesis Defense
University of Georgia, Athens, GA, March 2022 - An Intorduction to the Erdős Multiplication Table Problem
Graduate Student Summer Conference
University of Georgia, Athens, GA, August 2021 - Guass’ Circle Problem
Presentation for MATH 8850
University of Georgia, Athens, GA, December 2020 - Multiplicative Order and Repeating Decimals
Graduate Student Summer Conference
University of Georgia, Athens, GA, July 2020 - On the distribution of pseudoprimes and Carmichael Numbers
Oral Exam Talk
University of Georgia, Athens, GA, Feb 2020 - Joints Problem
Analysis Reading Seminar
University of Georgia, Athens, GA, Oct 2019 - Zeta Functions
SMARTS Seminar
University of Georgia, Athens, GA, Oct 2019 - Orders of Arithmetic Functions
Graduate Student Seminar
University of Georgia, Athens, GA, April 2019 - Collatz Conjecture and its Polynomial Analogue
Graduate Student Summer Conference
University of Georgia, Athens, GA, July 2018