Publications & Preprints
Counting totally imaginary number fields. (With Qiyao Yu.) Preprint, 2024.
Motives, Periods, and Functoriality. (With Pierre Deligne.) Preprint, 2023.
Eisenstein cohomology for GL(N) and the special values of Rankin-Selberg L-functions over a totally imaginary number field. Preprint, 2023.
Eisenstein cohomology for orthogonal groups and the special values of L-functions for O(2n) x GL(1). (With Chandhrasheel Bhagwat.) Preprint, 2022.
Ramanujan's congruence primes. (With Ellise Parnoff.) To appear in Involve, A Journal of Mathematics.
Notes on the arithmetic of Hecke L-functions. Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 132 (2022), no. 2, Paper no. 71, 37 pages.
An arithmetic property of intertwining operators for p-adic groups. Canadian Journal of Mathematics, 75 (2023), no. 1, 83-107.
Special values of L-functions of GL(n) over a CM field. International Mathematical Research Notices, IMRN 2022, no. 13, 10119-10147.
L-functions for GL(2n): p-adic properties and nonvanishing of twists. (With Mladen Dimitrov and Fabian Januszewski). Compositio Mathematicae, 156 (2020), no. 12, 2437-2468.
Eisenstein cohomology for GL(N) and ratios of critical values of Rankin-Selberg L-functions. (With Günter Harder). Annals of Mathematics Studies, 203, Princeton University Press, Princeton, 2020.
Cohomological representations and functorial transfer from classical groups. (With Makarand Sarnobat). Cohomology of aruthmetic groups, 157-176, Springer Proc. Math. Stat., 245, Springer, Cham, 2018. Special volume in honour of Joachim Schwermer's 60th birthday.
Critical values of L-functions for GL(3) x GL(1) over a totally real field. (With Gunja Sachdeva). L-functions and automorphic forms, 195-230, Contrib. Math. Comput. Sci., 10, Springer, Cham, 2017.
Endoscopy and the Cohomology of GL(n). (With Chandrasheel Bhagwat). Bulletin of Iranian Mathematical Society, 43 (2017), no. 4, 317-335. Special volume in honor of Freydoon Shahidi's 70th birthday.
Special values for L-functions for orthogonal groups. (With Chandrasheel Bhagwat). C. R. Math. Acad. Sci. Paris., 355 (2017), No. 3, 263-267.
Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field. (With Baskar Balasubramanyam). American Journal of Mathematics, 139 (2017), No. 3, 641-679.
p-adic L-functions for GL(n). (With Debargha Banerjee). In "p-adic aspects of modular forms," World Scientific Press, 237--277, (2016).
Critical values for Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2). Forum Mathematicum, 28 (2016) No. 3, 457-489.
Special values of the Riemann zeta function: some results and conjectures. Bloch-Kato conjecture for the Riemann zeta function. 1-21. London Math. Soc., Lecture Note Series, Vol 418, Cambridge University Press, Cambridge (2015).
Comparison results for certain periods of cusp forms on GL(2n) over a totally real number field. The legacy of Srinivasa Ramanujan, 323-334, Ramanujan Math. Soc. Lect. Notes Ser., 20, Ramanujan Math. Soc., Mysore, 2013.
On the arithmetic of Shalika models and the critical values of L-functions for GL(2n). (With Harald Grobner) With an appendix by Wee Teck Gan. American Journal of Mathematics, 136 (2014) 675--728. (Published by Johns Hopkins University Press.)
On some arithmetic properties of automorphic forms of GL(m) over a division algebra. (With Harald Grobner) International Journal of Number Theory, Vol. 10, No. 4, (2014) 963--1013. (Published by World Scientific Publishing Company.)
Arithmeticity for periods of automorphic forms. (With Wee Teck Gan) Automorphic Representations and L-functions, 187--229, Tata Inst. Fund. Res. Stu. Math. No. 22, TIFR, Mumbai (2013). (Published by Hindustan Book Agency.)
Ratios of periods for tensor product motives. (With Chandrasheel Bhagwat) Mathematics Research Letters, 20 (2013) No. 4, 615-628. (Published by International Press, Boston, Inc.)
Notes on the arithmetic of Hilbert modular forms. (with Naomi Tanabe) J. Ramanujan Math. Soc. 26 (2011), no. 3, 261–319.
Eisenstein Cohomology and ratios of critical values of Rankin-Selberg L-functions. (With Günter Harder) C. R. Math. Acad. Sci. Paris 349 (2011), no. 13-14, 719–724.
A cuspidality criterion for the exterior square transfer for cusp forms on GL(4). (With Mahdi Asgari) On certain L-functions, 33–53, Clay Math. Proc., 13, Amer. Math. Soc., Providence, RI, 2011.
On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-functions of modular forms. Int. Math. Res. Not. IMRN 2010, no. 2, 334–372.
On certain period relations for cusp forms on GL(n). (With Freydoon Shahidi) Int. Math. Res. Not. 2008, Art. ID rnn 077, 23 pp.
Functoriality and special values of L-functions. (With Freydoon Shahidi) Eisenstein series and applications, 271–293, Progr. Math., 258, Birkhäuser Boston, Boston, MA, 2008.
Representation theory of GL(n) over non-Archimedean local fields. (With Dipendra Prasad) School on Automorphic Forms on GL(n), 159–205, ICTP Lect. Notes, 21, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2008.
On the restriction to D* x D* of representations of p-adic GL(2,D). Canadian Journal of Mathematics, 59 (2007), no. 5, 1050–1068.
A Künneth theorem for p-adic groups. Canadian Mathematical Bulletin, 50 (2007), no. 3, 440–446.
Conductors and newforms for SL(2). (With Joshua Lansky) Pacific Journal of Mathematics, 231 (2007), no. 1, 127–153.
Nonvanishing of L-functions of cusp forms inside the critical strip. Number theory, 97–105, Ramanujan Math. Soc. Lect. Notes Ser., 1, Ramanujan Math. Soc., Mysore, 2005.
Conductors and newforms for U(1,1). (With Joshua Lansky) Proc. Indian Acad. Sci. Math. Sci. 114 (2004), no. 4, 319–343.
On the correspondence of representations between GL(n) and division algebras. (With Joshua Lansky) Proc. Amer. Math. Soc. 131 (2003), no. 5, 1641–1648.
On representations of p-adic GL(2,D). Pacific Journal of Mathematics, 206 (2002), no. 2, 451–464.
Nonvanishing of certain Rankin-Selberg L-functions. C. R. Math. Acad. Sci. Soc. R. Can. 24 (2002), no. 2, 67–71.
Kirillov theory for GL(2,D). Cohomology of arithmetic groups, L-functions and automorphic forms (Mumbai, 1998/1999), 143–157, Tata Inst. Fund. Res. Stud. Math., 15, Tata Inst. Fund. Res., Bombay, 2001.
Some variations on the Dedekind conjecture. (With Ram Murty) Journal of Ramanujan Mathematical Society, 15 (2000), no. 4, 225–245.
Kirillov theory for GL(2,D) where D is a division algebra over a non-Archimedean local field. (With Dipendra Prasad) Duke Mathematical Journal, 104 (2000), no. 1, 19–44.
Some other writings
My PhD thesis. It is about the representation theory of GL(2,D) for a p-adic division algebra D.
Groups acting on trees. Notes on Bass-Serre Theory. (With B. Sury) Based on a short course of lectures at IIT-Guwahati.
Exercises in Representation Theory. Based on a course taught at the University of Iowa.