PUBLICATIONS AND PREPRINTS

1. An Analogue of the Dedekind Eta Function for Hecke Groups H(√D) (with Dorian Goldfeld, Nicolas Robles & Alexandru Zaharescu), submitted (2025). [pdf] [Arxiv]

2. On Page's Theorem and Zero-Free Regions for Dirichlet L-functions (with Kyle Pratt), submitted (2025). [pdf] 

3. Distributions Associated to Small Quadratic Non-Residues and their Partitions (with Bruce Berndt & Alexandru Zaharescu), submitted (2025). [pdf] 

4. Surfaces Associated to Zeros of Automorphic L-functions (with Cruz Castillo & Alexandru Zaharescu), submitted (2024). [pdf]

Companion website to the above paper, containing extended numerical data, computational results, and interactive visualizations of Correlation Surfaces

5. Non-Vanishing of Dirichlet L-functions with Moduli in Short Intervals and Arithmetic Progressions (with Alexandru Zaharescu), submitted (2024). [pdf] [Arxiv] 

6. Representations as Sums of Icosahedral and Dodecahedral Numbers : Proof of Pollock's Conjectures (with Anji Dong, Katerina Saettone & Alexandru Zaharescu), Int. Math. Res. Not. IMRN. accepted for publication (2025). [DOI] [pdf] 

7. Remarks on Landau-Siegel zeros (with Jesse Thorner & Alexandru Zaharescu), Algebra Number Theory. accepted for publication (2024). [pdf] [Arxiv] 

8. Exponential Sums over Möbius Convolutions with Applications to Partitions (with Nicolas Robles & Alexandru Zaharescu), Canad. J. Math. accepted for publication (2024). [DOI] [pdf] [Arxiv] 

9. Connections between Number Theory and the Theory of Turbulence (with an appendix by Alexander Migdal) (with Alexandru Zaharescu), Communications in Number Theory & Physics. Vol 19. No. 2. pp. 415-471. (2025). [DOI] [pdf]

10. Poisson Behavior for Chains of Small Quadratic Non-Residues (with Kunjakanan Nath & Alexandru Zaharescu), Int. Math. Res. Not. IMRN. Vol. 2024, No. 4, pp. 3356-3390. [DOI] [pdf] 

11. Gaussian Phenomena for Small Quadratic Residues and Non-Residues (with Kunjakanan Nath & Alexandru Zaharescu), Trans. Amer. Math. Soc. Vol. 376 (2023), no. 5, pp. 3695–3724. [DOI] [pdf] 

12. Multiple Zeta Functions and Polylogarithms over Global Function Fields (with Nicolas Degré Pelletier & Matilde Lalín), J. Théorie Nombres Bordeaux. 32, (2020), no. 2, pp. 403-438. [DOI] [pdf]

DISSERTATIONS

1. Ph.D. Dissertation. Title : Topics in the Theory of Automorphic L-functions. [pdf]

Supervised by Prof. Alexandru Zaharescu and Prof. Jesse Thorner, University of Illinois Urbana-Champaign (2025). 

2. Masters Dissertation. Title : Arithmetic properties of j-invariant of Lattices with CM. [pdf]

Supervised by Dr. Swarnendu Datta, Indian Institute of Science Education and Research Kolkata (2020).