My research interest includes study of p-adic family of modular (automorphic) forms and Galois representations, Selmer groups, p-adic L functions. Also I am interested questions regarding class groups of number fields.
Publication and Preprints
17. With D. De & S. Mondal, Relative p-class groups and p-Selmer groups, available on arXiv.
16. With S. Jha & P. Shingavekar, $\sqrt{-3}$-Selmer groups, ideal class groups and large 3-Selmer ranks, available on arXiv. To appaer in The Ramanujan Journal.
15. With S. Jha & B. Sury, Binary Cubic Forms and Rational Cube Sum Problem, available on arXiv. To appear in Proceedings of the AMS. DOI: https://doi.org/10.1090/proc/17366
14. With S. Jha & P. Shingavekar, 3-Selmer groups, ideal class groups and cube sum problem. Journal of Number Theory, 277, (2025), 165-200 . Older version , available on arXiv.
13. With S. Jha & D. Kundu, Hilbert's 10th problem via Mordell curve, available on arXiv. Appeared online in Canadian Math. Bulletin.
12. With S. Panda, On characteristic ideal of Selmer group associated to Artin representations, Journal of Ramanujan Mathematical Society, 39 (2024), No. 2, 109-129. Older version available on arXiv.
11. With T. Kathiravan and U.K. Sangale, Infinite families of congruences modulo 2 for (l,k)-regular partitions, Hardy-Ramanujan Journal, 46 (2023), 51-62.
10. With P. Shingavekar, Cube sum problem for integers having exactly two distinct prime factors, Proceedings of Indian Academy of Sciences, 133 (2023), No. 2, 22 pages. Older version available on arXiv.
9. With B. Sury, Fruit Diophantine Equation , The Math. Gazette, 107, No. 569 (2023),302-306. Older version available on arXiv.
8. With B. Sury, Cyclic cubic extensions of Q, International Journal of Number Theory 18, No. 9 (2022), 1929-1955. Older version available on arXiv.
7. With S. Jha and S. Shekhar, p^r Selmer companion modular forms, Annales de L'institut Fourier 71, No. 1 (2021), 53-87. Older version available on arXiv.
6. With B. Baskar, p-adic Asai transfer, Journal of Ramanujan Mathematical Society 34, No.3 (2019) 305-324. Older version available on arXiv.
5. With B. Baskar, Ordinary families of automorphic forms on definite unitary groups, p-adic aspects of modular forms, (2016) 65-120.
4. With S. Jha, Functional equation for the Selmer group of nearly ordinary Hida deformation of Hilbert modular forms, Asian Journal of Mathematics 21(3) (2017) 397-428, older version available on arXiv.
3. Endoscopic transfer between eigenvarieties for definite unitary groups, Journal of Ramanujan Mathematical Society 31, No.3 (2016) 235–255, available on arXiv.
2. With M. Kulkarni and B. Sury, l-Class groups of cyclic extensions of prime degree l, Journal of Ramanujan Mathematical Society 30, No.4 (2015) 413–454, older version available on arXiv.
1. Geometry of the eigencurve at critical Eisenstein series of weight 2 , Journal de Théorie des Nombres de Bordeaux 27(2015), 183-197, older version available on arXiv.
My PhD thesis can be accessed here , or you can send me an email for a copy if you can not access it. Please be aware of a lot of typos if you are planning to read it.