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.
Jan 2021: MA 215, Introduction to Modular forms:
These would be expanded and polished extensively -- but you are strongly advised to consult these notes to judge it's content before deciding to opt for the course.
The meeting link can be found from the Maths dept. Intranet.
Send an email to me if you want to attend.
Meeting: Tuesday-Thursday, 3.30-5.00 pm.
**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 11 June , from 2 PM to 5 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.
(a) Practice problems: 10%
(b) Quizzes: 30%
(c) Mid-term: 30%
(d) Final-term: 30%
On fundamental Fourier coefficients of Siegel modular forms. (with S. Böcherer), 48 pp. J. Inst. Math. Jussieu, to appear. https://doi.org/10.1017/S1474748021000086
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. Ramanujan J., to appear.
On Fourier coefficients of elliptic modular forms mod l with applications to Siegel modular forms (with. S. Böcherer), 32pp. Manuscripta Math., https://doi.org/10.1007/s00229-021-01277-8
On the sup-norm of Maass 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)