Research interests

Analytic number theory, automorphic forms, partitions, quadratic forms.

  Publications

1. Sails for universal quadratic forms. (with V. Kala)
   Submitted for publication. (arXiv)

2. Universal quadratic forms and Northcott property of infinite number fields. (with N. Daans, V. Kala)
   Submitted for publication. (arXiv)

3. Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields.
   Adv. Math. 447 (2024), 109694. (arXiv)

4. Distribution of parity differences in partitions into distinct parts.
   Submitted for publication. (arXiv)

5. Asymptotics of parity biases for partitions into distinct parts via Nahm sums. (with K. Bringmann, L. Rolen, M. Storzer)
   Submitted for publication. (arXiv)

6. Unimodality of ranks and a proof of Stanton's conjecture. (with K. Bringmann, L. Rolen)
   Submitted for publication. (arXiv) (List of constants here)

7. Bounds for Kloosterman sums on GL(n). (with V. Blomer)
   Math. Ann. (2023). (arXiv)

8. A Density Theorem for Sp(4).
   J. London Math. Soc. 105(4) (2022), 2047-2075. (arXiv) (corrigenda)

9. Symplectic Kloosterman sums and Poincaré series.
   Ramanujan J. 57 (2022), 707-753. (arXiv)

10. Fourier coefficients of Sp(4) Eisenstein series.
    Acta Arith. (2024) (arXiv)

11. Interesting identities involving weighted representations of integers as sums of arbitrarily many squares. (with M. Jang, B. Kane, W. Kohnen)
    Proc. Natl. Acad. Sci. (USA) 116(39) (2019), 19374-19379. (arXiv)

12. The Bruinier–Funke pairing and the orthogonal complement of unary theta functions. (with B. Kane)
    in J. Bruinier, W. Kohnen (Eds.), ''L-functions and automorphic forms'', Contributions in mathematical and computational sciences 10 (2017), Springer, 139-157. (arXiv)

Thesis

Symplectic automorphic forms and Kloosterman sums. Doctoral thesis, Universität Bonn (2021). (Link)

Miscellaneous

1. Almost Universal Weighted Ternary Sums of Polygonal Numbers. (with A. Mehta) (arXiv)