Associate Professor, Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India.
Research interests: Analytic aspects of Automorphic forms, analytic and algebraic number theory.
~If someone does science in a forest, but doesn't make a sound, did science actually happen?
- Michael Short.
1) Pramath Anamby (2014 --) (IISc)
2) Ritwik Pal (2014 --) (IISc)
3) K. Hariram (2016 --) (IISc)
Sushma Palimar (DST Women Scientist, 2017--),
Abhash Kr. Jha (SERB-NPDF, 2017--),
Sneh Bala Sinha (NBHM PostDoc, 2018--).
Msc : Vignesh AH (2015), A. Dasgupta (2018)
UG : Final Year projects: Chirag (2014), Debatosh Das (2016)
Jan 2019: MA 213, Algebra II: Grading policy - There would be no written assignments to be turned in. However, there would be periodical quizzes (say of duration 30-45 mins conducted by the T.A.) followed by discussion of these and other practice problems, which would be put up on this webpage periodically.
Approximately the weightage would be: 25%, 25%, 50% for Quizzes, Mid-term exam, Final-exam respectively. The TA for this course is G. V. K. Teja (with assistance from M Hassain).
* The mid semestral examination has been scheduled during 18-23 Feb. on 23 Feb. from 10AM-1 PM in LH-1. The syllabus would be whatever was covered in class until 14 February.
**Practice problems should be considered as supplements to the class, and are examinable, unless mentioned otherwise. You can ask about any of them to either the T.A. or the instructor.
***Final exam would be held on ?? April, from ??AM to ?? PM. Venue would be .... Please write short answers. Short and correct answers would be given high value. In particular there is no point in deriving or proving things which have already been proved in class. You may just state them.
(c) Solutions: S1
(c) Mid-term: M1, F1
- On fundamental Fourier coefficients of Siegel modular forms. (with S. Böcherer), 39pp.
- Omega results for Fourier coefficients of half-integral weight and Siegel modular forms, 14pp. to appear in Springer Conf. Proceedings (intended for the conference proc. at KSOM commemorating the 60th birthday of Prof. M. Manickam).
- Large Hecke eigenvalues and an Omega result for non Saito--Kurokawa lifts (with P. Anamby, R. Pal), 13pp.
- On Fourier coefficients of elliptic modular forms mod l with applications to Siegel modular forms (with. S. Böcherer), 31pp.
- Sup-norm bounds for Jacobi forms of index 1 and for Saito-Kurokawa lifts. RMS lecture Notes (2020) for conference proceedings at IIT ROPAR, (with J. Sengupta).
Hecke-Siegel type threshold for square-free Fourier coefficients: an improvement RIMS Kokyuroku Kyoto Univ., proceedings for the conference “Analytic and Arithmetic Theory of Automorphic Forms”, January 2018. (With P. Anamby)
MR4034598 Das, Soumya; Jha, Abhash Kumar Analytic properties of twisted real-analytic Hermitian Klingen type Eisenstein series and applications. Abh. Math. Semin. Univ. Hambg. 89 (2019), no. 2, 105–116. 11F55 (11F66)
MR3908796 Anamby, Pramath; Das, Soumya Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients. Publ. Mat. 63 (2019), no. 1, 307–341. (Reviewer: Brundaban Sahu) 11F30 (11F50 11F55)
MR3825472 Anamby, Pramath; Das, Soumya Bounds for the Petersson norms of the pullbacks of Saito-Kurokawa lifts. J. Number Theory 191 (2018), 289–304. (Reviewer: Karam Deo Shankhadhar) 11F11 (11F46 11F66)
MR3798786 Das, Soumya; Kohnen, Winfried On sign changes of eigenvalues of Siegel cusp forms of genus 2 in prime powers. Acta Arith. 183 (2018), no. 2, 167–172. (Reviewer: Tomoyoshi Ibukiyama) 11F46 (11F41)
MR3477047 Das, Soumya; Ganguly, Satadal A note on small gaps between nonzero Fourier coefficients of cusp forms. Proc. Amer. Math. Soc. 144 (2016), no. 6, 2301–2305. (Reviewer: Cherng-tiao Perng) 11F30 (11F11 11G05)
MR3385236 Das, Soumya; Khan, Rizwanur Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions. J. Ramanujan Math. Soc. 30 (2015), no. 3, 237–250. (Reviewer: Sanoli Gun) 11F11 (11F66)
MR3365786 Das, Soumya; Sengupta, Jyoti L∞ norms of holomorphic modular forms in the case of compact quotient. Forum Math. 27 (2015), no. 4, 1987–2001. (Reviewer: Guangshi Lü) 11F11 (11F12) (update: use this version PDF)
MR3280046 Böcherer, Siegfried; Das, Soumya Linear independence of Poincaré series of exponential type via non-analytic methods. Trans. Amer. Math. Soc. 367 (2015), no. 2, 1329–1345. (Reviewer: Sheng-Chi Liu) 11F30 (11F46)
MR3201897 Böcherer, Siegfried; Das, Soumya Characterization of Siegel cusp forms by the growth of their Fourier coefficients. Math. Ann. 359 (2014), no. 1-2, 169–188. (Reviewer: Rainer Schulze-Pillot) 11F30 (11F46)
MR3182539 Das, Soumya; Kohnen, Winfried; Sengupta, Jyoti On a convolution series attached to a Siegel Hecke cusp form of degree 2. Ramanujan J. 33 (2014), no. 3, 367–378. (Reviewer: Suzanne Caulk) 11F46 (11F66)
MR3221309 Das, Soumya; Kohnen, Winfried Some remarks on the Resnikoff-Saldaña conjecture. The legacy of Srinivasa Ramanujan, 153–161, Ramanujan Math. Soc. Lect. Notes Ser., 20, Ramanujan Math. Soc., Mysore, 2013. (Reviewer: Jae-Hyun Yang) 11F30 (11F46)
MR3065087 Böcherer, Siegfried; Das, Soumya On holomorphic differential operators equivariant for the inclusion of Sp(n,R) in U(n,n). Int. Math. Res. Not. IMRN 2013, no. 11, 2534–2567. (Reviewer: Rolf Berndt) 32M15 (11F03 32W50)