Publications

Research articles:-

1. CROSSED PRODUCT ALGEBRAS ATTACHED TO WEIGHT ONE FORMS (joint with Eknath Ghate), Mathematical Research Letters, Volume 18, issue 1, January 2011.

2. ADJOINT LIFTS AND MODULAR ENDOMORPHISM ALGEBRAS (joint with Eknath Ghate), Israel Journal of Mathematics, June 2013, Volume 195, Issue 2, 507-543. 

3. A note on the Eisenstein elements for prime square level, Proceedings of the American Mathematical Society. 142 (2014), 3675-3686.http://dx.doi.org/10.1090/S0002-9939-2014-12097-1

4. Differential modular forms on the Shimura curves over totally real fields, Journal of Number theory. http://www.sciencedirect.com/science/article/pii/S0022314X13002412

5. 1. The Eisenstein elements for level product of two odd primes, joint with S. Krishnamoorthy, the Pacific Journal of Mathematics, Vol. 281, No. 2, 2016. 

6. The Eisenstein cycles as modular symbols, joint with Loic Merel,  the Journal of the London Mathematical Society: 

https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12136

7. Supercuspidal ramifications and traces of adjoint lifts, joint with Tathagata Mandal, Journal of Number theory: 

https://www.sciencedirect.com/science/article/pii/S0022314X19300939?via%3Dihub

8.  A note on quadratic twisting of epsilon factors for modular forms with arbitrary nebentypus, joint with Tathagata Mandal. To appear in the Proceedings of the American Mathemical Society, Volume 148, Number 4, April 2020, Pages 1509–1525. 

https://www.ams.org/journals/proc/0000-000-00/S0002-9939-2020-14887-3/S0002-9939-2020-14887-3.pdf

9. Semi-stable models of modular curves $X_0(p^2)$ and some arithmetic applications, joint with Chitrabhanu Chaudhuri. To appear in the Israel Journal of Mathematics.  

10. Self intersection numbers  of minimal regular models of  modular curves $X_0(p^2)$ over rational numbers, joint with  Diganta Borah  and Chitrabhanu Chaudhuri, to appear in the journal Mathematische Zeitschrift. https://link.springer.com/article/10.1007/s00209-020-02480-1

11. Differential modular forms over totally real fields of integral weights, joint with Arnab Saha, Research in number theory. https://link.springer.com/article/10.1007/s40993-021-00269-7.

https://www.worldscientific.com/doi/epdf/10.1142/S179304212450009X

12. Towards a mod-p Lubin-Tate theory for  GL_2 over totally real fields, joint with Vivek Rai

https://arxiv.org/abs/2206.09706

International journal of number theory (IJNT). 

13. THE EISENSTEIN CYCLES AND MANIN-DRINFELD PROPERTIES, joint with Loic Merel. 

https://arxiv.org/abs/2204.06379

Forum Mathematicum. 

https://www.degruyter.com/document/doi/10.1515/forum-2022-0116/html

14. 2. THE HEISENBERG COVERING OF THE FERMAT CURVE, joint with Loic Merel. 

https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/heisenberg-covering-of-the-fermat-curve/EB99FD41F223676B87044DBAE7713EB5

Canadian Journal of Mathematics. 

15. Modular forms with non-vanishing central values and linear independence of Fourier coefficients, joint with Priyanka Majumder, the Ramanujan Journal. 

Expository articles:-

1.  LAMBDA-ADIC FORMS AND THE IWASAWA MAIN CONJECTURE joint with V. G. Narasimha Kumar Cheraku and Eknath Ghate,  Iwaswa Theory of Totally real Fields, (Proceedings of a Workshop held at IIT Guwahati, published by Ramanujan Mathematical Society) 2010, No. 12.

2.  $p$-adic $L$-function on $\GL_n$, joint with A. Raghuram, conference proceedings of the $p$-adic aspects of modular forms, IISER, Pune, 2016.