Publications/Preprints/Ongoing

Analytic number theory

• Parity questions concerning the generalized divisor function involving small prime factors (with Krishna Alladi), submitted. 

• On a partial sum related to the Euler totient function, submitted.

• Gauss circle problem over smooth integers, New York J. Math., 30 (2024), 270-294.

q-series and partitions

• Strong q-analogues for values of the Dirichlet beta function (with Tim Huber), submitted.

• Resurgence of Habiro elements (with Samuel Crew, Robert Osburn), submitted. 

• Asymptotics and sign patterns for coefficients in expansions of Habiro elements (with Abhash Kumar Jha, Byungchan Kim, Robert Osburn), Math Z., 304, 57 (2023).

• Combinatorial identities associated with a bivariate generating function for overpartition pairs (with Atul Dixit), Adv. Appl. Math., 143, 102444 (2022).

• Congruences for some partition functions (with Abhash Kumar Jha), J. Ramanujan Math. Soc., 37, No.3 (2022) 241–256.

• Some identities for the partition function (with Abhash Kumar Jha, Anup Kumar Singh), SAGE file  Mathematica file, J. Math. Anal. Appl., 508 (1), 125864 (2022).

• Quantum modularity of partial theta series with periodic coefficients (with Robert Osburn), Forum Math., 33, no. 2, pp. 451-463 (2021).

• Congruences for generalized Fishburn numbers at roots of unity, Acta Arith., 199, 77-102 (2021).

• On sums of coefficients of polynomials related to the Borwein conjectures (with Venkata Raghu Tej Pantangi), Ramanujan J., 57 : 369–387 (2022).

• Some formulae for coefficients in restricted q-products (with Venkata Raghu Tej Pantangi), J. Number Theory, 219, pages 283-299 (2021).

• A q-analogue for Euler's ζ(6)=π^6/945, Ann. Comb., 23, pages 801–806 (2019).

• A q-analogue for Euler’s evaluations of the Riemann zeta function, Res. Number Theory,  5, Article number: 3 (2019). 

In Preparation

• Congruences for coefficients in expansions of certain q-hypergeometric series* (with Yuliann Sepulveda), in preparation.

• On the generalized divisor function involving small and large prime factors of integers: A duality principle, in preparation.

• A note on expressing certain Eisenstein series using Eulerian polynomials, in preparation.

• Bell polynomials and partition identities*, in preparation.

* titles might be slightly different in the final version.