Research

Fields of Interest: Number theory, arithmetic geometry, and algebraic geometry.

Publications

• • Multiplicative structures of shifted multiplicative subgroups of finite fields (with C.H. Yip and S. Yoo), submitted.

  • On Markoff type surfaces over number fields and the arithmetic of Markoff numbers (with D. Schindler and J. Sivaraman), submitted.

  • Building bridges between Tate conjectures and arithmetic invariants (with V. Cantoral-Farfan), submitted.

  • k-Diophantine m-tuples in finite fields (with T. Hammonds, S. J. Miller, A. Nigam, K. Onghai, D. Saikia, L. M. Sharma), Int. J. Number Theory 19, no. 4, 891–912 (2023).

  • On the Birch and Swinnerton-Dyer conjecture (with M. R. Murty), Math. Comp. 92, no. 339, 385–408 (2023).

  • The Sato-Tate conjecture and Nagao's conjecture, J. Number Theory 242, 245–277 (2023).

  • On the density of irreducible polynomials which generate k-free polynomials over function fields (with M. R. Murty), Finite Fields Appl. 78 (2022).

  • Corrigendum to "Artin's primitive root conjecture for function fields revisited'' (with M. R. Murty), Finite Fields Appl. 78 (2022).

  • On the generalised Diophantine m-tuples (with A. Dixit and M. R. Murty), Proc. Amer. Math. Soc. 150 (2022).

  • Artin's primitive root conjecture for function fields revisited (with M. R. Murty), Finite Fields Appl. 67, (2020).

  • Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture (with T. Hammonds, B. Logsdon, Á. Lozano-Robledo, S. J. Miller), Journal of Number Theory, 215, 339-361, (2020). 

  • Elliptic Fermat numbers and elliptic divisibility sequences (with A. Walsh), INTEGERS, 20, #A29, (2020).

  • The Density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their index, Journal of Number Theory, 207, 22-41, (2020). 

  • The distribution of the trace of Frobenius and its applications in number theory, Brown University, (2019).