My research interest broadly comes under the Langlands
Program. In particular, I am interested in understanding classical
modular forms and automorphic representations associated to them. Below
is the list of my papers and preprints.
- Lifting from SL̃(2) to GSpin(1, 4), Int. Math. Res. Not. 63, 3919-3966 (2005) (pdf).
- Sign changes of
Hecke eigenvalues of Siegel cusp forms of degree 2, Proc.
of Amer. Math. Soc. 136, 3831-3838 (2008) (with Ralf Schmidt) (pdf).
-
Ramanujan type results
for Siegel cusp forms of degree 2, J. of Ramanujan Math.
Soc., 24, No. 1, 87-111 (2009) (with Ralf Schmidt) (pdf).
- Jacobi Maass Forms, Abh. Math. Sem. Univ.
Hamburg, 79, 87-111 (2009) (pdf).
- Integral representation
for L-functions for Gsp(4) x GL(2), J. Number Theory, 129,
1272-1324 (2009) (with Ralf Schmidt) (pdf)
- Bessel models for
lowest weight representations of GSp(4, R), Int. Math. Res.
Not., 7, 1159-1212 (2009) (with Ralf Schmidt) (pdf)
- Classical interpretation of the Ramanujan
conjecture for Siegel cusp forms of genus n, Manuscr.
Math., 130, Issue 2, 225-231 (2009) (pdf)
- Steinberg representation of
GSp(4): Bessel models and integral representation of L-functions, Pacific Journal of Mathematics, Vol 250, no. 2, 365-406 (2011) (pdf). A longer version is available here.
- Special values of L-functions for Saito-Kurokawa lifts , Mathematical Proceedings of the
Cambridge Philosophical Society, Vol 155, Issue 2, 237-255 (2013) (with James L. Brown)(pdf).
- Irreducibility Criteria for Local and Global Representations, Proc. of Amer. Math. Soc. 141, no 1, 55-63 (2013) (with Hiro-aki Narita and Ralf Schmidt) (pdf).
- Talking Mathematics: An abstract algebra professors teaching diaries, Research in Undergraduate Mathematics Education (RUME) conference, Denver, Colorado Feb 21-24 (2013) (with John Paul Cook, Ralf Schmidt, Sepideh Stewart).
- Bounds for Rankin Selberg integrals and quantum unique ergodicity for powerful levels, J. Amer. Math. Soc., 27, 141-191 (2014) (with Paul Nelson and Abhishek Saha) (pdf).
- Transfer of Siegel cusp forms of degree 2, Mem. Amer. Math. Soc., Volume 232, Number 1090 (2014) (with Abhishek Saha and Ralf Schmidt) (pdf).
- Bessel models for GSp(4): Siegel vectors of square-free level, J. Number Theory, 136, 134-164 (2014) (with Ralf Schmidt) (pdf), a longer version is available here.
- Characterization of the Saito-Kurokawa lifting : a survey, Rocky Mountain J. Math. 43 (2013), 1747-1757 (with David Farmer, Nathan Ryan and Ralf Schmidt) (pdf).
- Living it up in the formal world: An abstract algebraist's teaching journey, submitted (with John Paul Cook, Ralf Schmidt, Sepideh Stewart).
- Representations of SL(2,R) and nearly holomorphic modular forms, Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1973, 141-154 (2015) (with Abhishek Saha and Ralf Schmidt) (pdf)
- Lifting to GL(2) over a division quaternion algebra and an explicit construction of CAP representations, Nagoya Mathematical Journal, 222, pp 137-185 (2016) (with Masanori Muto and Hiro-aki Narita) (pdf)
- Glycemic Variability is associated with markers of vascular stress in adolescents The Journal of Pediatrics, May 2016, Volume 172, Pages 47-55 DOI: http://dx.doi.org/10.1016/j.jpeds.2016.01.065 (with Paul Desari, Benjamin Gandomani, April Teague, Michael Otto, Kevin Short)
- Test vectors for GL(2) and applications to L-values, Algebra and Number Theory 11, no. 2, 253-318 (2017) (with Daniel File and Kimball Martin) (pdf).
- Local and global Maass relations, Mathematische Zeitschrift 287, no. 1-2, 655-677 (with Abhishek Saha and Ralf Schmidt) (pdf) An expanded version is available here.
- A note on the growth of nearly holomorphic vector-valued Siegel modular forms , L-functions and automorphic forms, Contributions to Mathematics and Computer Science 10, (2018) (with Abhishek Saha and Ralf Schmidt) (pdf)
- Multiplicity one for L-functions and applications, submitted arXiv:1305.3792 (with David Farmer, Nathan Ryan and Ralf Schmidt) (pdf).
- Lowest weight modules of Sp(4,R) and nearly holomorphic Siegel modular forms, preprint arXiv:1501.00524 (with Abhishek Saha and Ralf Schmidt) (pdf)
- Explicit refinements of Bocherer's conjecture for Siegel modular forms of square-free level, preprint arXiv:1512.07204 (with Martin Dickson, Abhishek Saha and Ralf Schmidt) (pdf)
- On the standard L-function for GSp(2n) x GL(1) and algebraicity of symmetric fourth L-values for GL(2), submitted arXiv:1803.06227 (with Abhishek Saha and Ralf Schmidt) (pdf)
- Restriction of Eisenstein series and Rankin-Selberg convolution, submitted arXiv:1706.09342 (with Rodney Keaton) (pdf)
- Analytic L-functions: Definitions, Theorems and Connections, submitted arXiv:1711.10375 (with David Farmer, Nathan Ryan and Ralf Schmidt) (pdf)
- An explicit construction of non-tempered cusp forms on O(1,8n+1), in preparation (with Yingkun Li and Hiro-aki Narita)
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