NISER

Number Theory

• Sato-Tate distribution for values of Gaussian hypergeometric functions and Hessian Curves, (with K. Ono, N. Saikia and H. Saad), (to appear in The Ramanujan Journal), (arXiv:2405.16349 ).
• The bias conjecture for elliptic curves over finite fields and Hurwitz class numbers in arithmetic progression, (with B. Kane and Z. Yang), (accepted for publication in Math. Ann.), (arXiv:2405.14234).
• Odd moments for the trace of Frobenius and the Sato–Tate conjecture in arithmetic progressions, (with K. Bringmann and B. Kane),
   Finite Fields and Their Applications, Volume 98, 2024, 102465.
• l-adic digits and class numbers of Imaginary quadratic fields,
  (with N. Saikia), International Journal of Mathematics Vol. 35, No. 11, 2450041 (2024).
• Zeros of higher derivatives of Riemann zeta function,
  (with M. K. Das), Journal of Mathematical Analysis and Applications, Volume 539, Issue 1, Part 2, 2024, 128531.
• Mean of the product of derivatives of Hardy's Z-function with Dirichlet polynomial, (with M.K. Das), J. Number Theory, 258 (2024), 334-367.
• An all-purpose Erdos-Kac theorem, (with M. R. Murty and V. K. Murty), Math. Z. 305, 45 (2023)
• A Bombieri-Vinogradov-type theorem for moduli with small radical, (with S. Baier), Acta Arithmetica 211 (2023), 173-184. (Arxiv link: arXiv:2212.0557).
• Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection (with B. Kane), Trans. Amer. Math. Soc. 376 (2023), 5503-5519. (Arxiv link: arXiv:2010.15325).
• Formulas for moments of class numbers in arithmetic progressions, (with K. Bringmann and B. Kane), Acta Arithmetica 207 (2023), 19-38. (Arxiv link: arXiv:2109.07325).
• Sato-Tate distribution of p-adic hypergeometric functions, (with N. Saikia), Res. number theory 9, 4 (2023).  (Arxiv link: arXiv:2207.10375).
• On signatures of elliptic curves and modular forms, (with A. Dąbrowski and J. Pomykała), The Ramanujan Journal (2023) 60:505-516.
• Turán inequalities for the plane partition function, (with K. Ono and L. Rolen), Advances in Mathematics, Volume 409, Part B, 2022, 108692. (Arxiv link: arXiv:2201.01352).
• A Bombieri-Vinogradov-type theorem with prime power moduli, (with S. Baier), Acta Arithmetica 204 (2022), 115-140.
• On the normal number of prime factors of sums of Fourier coefficients of eigenforms, (with M. R. Murty and V. K. Murty), J. Number Theory, 233 (2022), 59-77.
• Distribution of signs of Karatsuba's and generalized Davenport-Heilbronn $Z$-functions, with M. K. Das, J. Number Theory, 212 (2020), 409-447.
• Traces of Hecke operators in level 1 and p-adic hypergeometric functions, with N. Saikia, Ramanujan J 52, 519–539 (2020).doi:10.1007/s11139-019-00170-z.
• Some remarks on the coefficients of symmetric power L-functions, with B. Kumar and J. Meher, Automorphic Forms and Related Topics, Contemporary Mathematics, Vol. 732, American Mathematical Society, (2019), 155-164.
• Distinguishing pure representations by normalized traces, with M.K Pandey and J.P Saha, J. Number Theory, 195 (2019), 217--225.
• Zeros of L-functions attached to cusp forms of half-integral weight, with J. Meher and K.D Shankhadhar, Proc. Amer. Math. Soc., 147 (2019), 131-143.
• Zeros of $L$-functions attached to modular forms of half-integral weights, with J. Meher and K. Srinivas, Bull. Lond. Math. Soc., 49 (2017), 926-936.
• Distinguishing Hecke eigenforms, with M. R. Murty, Proc. Amer. Math. Soc., 145 (2017), 1899-1904.
• Sign changes of coefficients of certain Dirichlet series, with J. Meher and K. D. Shankhadhar, Funct. Approx. Comment. Math., 52 (2015), Part 1, 117–126.

Preprints:

• Distribution of rational points of an algebraic surface over finite fields, (with N. Saikia), (preprint) (arXiv:2410.17340).
• Effective joint equidistribution of eigenvalues of Hecke operators, (preprint). Arxiv link: arXiv:1703.07944.
• Distribution of gaps of eigenangles of Hecke operators, (preprint). Arxiv link: arxiv.org/pdf/1603.06249.pdf.

My research interests broadly encompass Probabilistic and Analytic Number Theory. In particular, I employ probabilistic and analytic techniques to investigate automorphic forms, the distribution of zeros of L-functions, half-integral weight modular forms, the equidistribution of number-theoretic objects, and exponential sums. More recently, I have developed an interest in post-quantum cryptography.

• Even Semester, 2024: M206 (Probability Theory).
• Odd Semester, 2023:  M205 (Linear Algebra).
• Even Semester, 2023: M561 (Elliptic Curves).
• Odd Semester, 2022: MA601 - Algebra I (Graduate course).
• Spring semester, 2022: M308 (Complex Analysis).