Research
Research
My research has focused on the analytic properties of arithmetic functions, applying techniques from analytic number theory, automorphic forms and the spectral theory.
[5] Vanishing properties of Kloosterman sums and Dyson's conjectures. The Ramanujan Journal, vol. 66, no. 50, 2025. [arXiv] [journal]
[4] Exact formulae for ranks of partitions, Transactions of the American Mathematical Society, accepted. [arXiv]
[3] Uniform bounds for Kloosterman sums of half-integral weight, same-sign case. Journal of Number Theory, vol. 274, 2025, pp. 104-139. [arXiv] [journal]
[2] Uniform bounds for Kloosterman sums of half-integral weight with applications. Forum Mathematicum, vol. 37, no. 1, 2025, pp. 75-109. [arXiv] [journal]
[1] (with O. González) Effective estimates for traces of singular moduli. Research in Number Theory, vol. 10, no. 29, 2024. [arXiv] [journal]
Not for publication
[2] Vanishing properties of Kloosterman sums and Dyson's conjectures, whole proof.
(This is the full version of [5] above, because the whole proof is long and tedious). [GitHub repository] (including the Mathematica files)
[1] Half-integral weight Kloosterman sums and integer partitions.
Ph.D. Thesis, University of Illinois, Urbana-Champaign, 2024. [PDF] [IDEALS - UIUC access (permalink)]