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, submitted. [arXiv]

[4] Exact formulae for ranks of partitions, submitted. [arXiv]

[3] Uniform bounds for Kloosterman sums of half-integral weight, same-sign case, submitted. [arXiv]

[2] Uniform bounds for Kloosterman sums of half-integral weight with applications, Forum Mathematicum, 2024, ahead of print. [arXiv] [journal]

[1] Effective estimates for traces of singular moduli (with O. González), 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Not for publication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]