Complex Analysis
Riemann Zeta Function ($\zeta(s)$), Transcendental Equations, and Holomorphic Dynamics.
Focus & Interests
My main research area focuses on Analytic Number Theory. I am particularly interested in the asymptotic behavior of arithmetic functions and the use of complex analysis tools to solve counting problems. More specifically, my interests can be divided into four main areas:
Number Theory
Sieve methods, distribution of prime numbers, and additive problems.
Combinatorics
Enumerative, Analytic, and Symbolic Combinatorics. Connections with generating functions.
Probability
Applications of probability to Analytic Number Theory, Random Matrices, and their unreasonable effectiveness.
Questions I'm interested in
- How can the Circle Method be generalized?
- What is the intrinsic relationship between probability and number theory?
- How is the Siewert-Burniston method applicable in different contexts?
Publications & Preprints
Papers in preparation.
Current Projects
Generalizations of the Hardy-Littlewood Circle Method
I am currently working on extending the ideas presented in my undergraduate thesis. The goal is to determine which properties are generalizable to different arithmetic sets.
Status: In progress