Here you will find mostly my mathematical work and possibly some other not so mathy works. Additionally, if I get around to it, I will post some class notes which I find worth sharing.
Disclaimer: There may possibly be errors in any of the preprints or notes I have posted; read them with a hint of skepticism, and comments are always welcome.
Publications
- The Basel Problem (PDF): This is a final project I completed in Complex Analysis at UC Berkeley. It builds up the necessary knowledge to solve the Basel problem in a few different ways and then leads to the derivation of the general formula for \( \zeta(2n) \) for \( n\in \mathbb{Z}_{>0} \).
- The Arithmetic Of The Zeta Function and its Generalizations (PDF): This is my senior honors thesis from UC Berkeley advised by Yunqing Tang. It should serve as a resource for advanced undergraduate or graduate students interested in studying analytic number theory, or more specifically, the arithmetic of the Riemann zeta function and its generalizations. It builds on my paper covering the Basel problem by analytically continuing the Riemann zeta function. We then discuss the irrationality of \( \zeta(3) \) and \( \zeta(2) \) due to both Apéry and Beukers. Then the definition of the irrationality exponent is discussed, Dirichlet's approximation theorem, the Dirichlet eta function, and the irrationality of \( \log(2) \). After this, we consider more current results related to the irrationality of the Riemann zeta function. In particular, we discuss Zudilin's 2018 result regarding the irrationality of at least one of \( \zeta(5), \zeta(7), \dots, \zeta(25) \). The last official part of the paper covers the analytic properties of the generalizations of the Riemann zeta function. In particular, we discuss the Hurwitz zeta function, Dirichlet \( L \)-functions, and the Dirichlet beta function (a specific Dirichlet \( L \)-function).
Course Notes
- Lecture Notes In Number Theory (PDF): (Unfinished) My goat ate about half of these.