Research Interests:   

• Arithmetic Geometry, Number Theory
• Graph Theory, Combinatorics

Publications :

• Modular degrees of elliptic curves & Watkin's conjecture (under preparation)
• Congruence classes for modular forms over small sets (with S. Bhakta and R. Muneeswaran) Accepted. To appear in the International Journal of Number Theory. arXiv:2302.02725
• Resistance distance in connected balanced graphs (with R. Balakrishnan and W. So). Discrete and Applied Mathematics, 2023 https://doi.org/10.1016/j.dam.2023.04.014
• A study on p-divisibility of class numbers of certain family of imaginary quadratic fields (with R. Muneeswaran) arXiv:2111.04387
• On the existence of euclidean ideal class in quadratic, cubic and quartic extensions (with P. Sunil Kumar). arXiv:2110.00225
• On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two (with P. Sunil Kumar). Archiv der Mathematik, 2023. https://doi.org/10.1007/s00013-022-01817-y
• On zero-sum subsequences of length exp(G) (with Umesh Shankar & Karthikesh). arXiv:2005.12042
• Note on the p-divisibility of class numbers of an infinite family of imaginary quadratic fields. (with P. Sunil Kumar), Glasgow Journal of Mathematics, 2022. https://doi.org/10.1017/S001708952100015X
• The Eisenstein and winding elements of modular symbols for odd square-free level. To appear in the Indian Journal of Pure and Applied Mathematics, 2022. http://rdcu.be/cZrf5
• Some congruences for (S,T)-regular bipartitions modulo T. (with T. Kathiravan), Integers, 2021. No. A15. 
• Some new congruences for l-regular partitions modulo 13, 17, and 23. (with S. Abinash and T. Kathiravan, Hardy-Ramanujan Journal, 2019, volume 42,73 – 84.
• Lifting congruences to weight 3/2 (with Neil Dummigan). Journal of Ramanujan Mathematical Society. Dec. 2017, 431– 440.
• A note on the coefficients of a Cohen-Eisenstein series, International Journal of Number Theory, vol. 12, no. 5, 2016, 1149 – 1161.
• On sign changes for almost prime coefficients of half-integral weight modular forms (with Ram Murty), Mathematika, vol 62, no. 03, 2016, 801 – 810.  
• On the Eisentein elements of level a product of two distinct primes(with Debargha Banerjee), Pacific Journal of Mathematics, 281, 2016, 257 – 285.
• On subfields of the modular function fields, Bulletin of Kerala Mathematics Association, 2013, 33 – 40.
• Powers of 2 in modular degrees of modular abelian varieties (with N. Dummigan), Journal of Number Theory, no.2. 2013, 501 – 522.
• On Davenport’s constant (with P. Rath and R. Thangadurai), International Journal of Number Theory, 2008, no. 1, 107 – 115.
• Modular degrees of elliptic curves, Proquest LLC, Ann Arbor, MI, 2011. Thesis (Ph.D.) - Sheffield University, U.K. 97 pp.