**Soumya Das**

*Associate Professor, Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India.*

*email: firstname.u2k@gmail.com,*

*firstname@iisc.ac.in*

**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.**

**Mentoring**

**Ph.D. :**

1) Pramath Anamby (2014 --) (IISc)

2) Ritwik Pal (2014 --) (IISc)

3) K. Hariram (2016 --) (IISc)

**Post-Docs : **

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)

*Reading Projects*:

**Summer students**

**Teaching**

**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.**

(a) Practice problems: P1, P2, P3, P4, A1 (to be submitted by few of you)

(b) Quizzes: Q1, Q2, Q3, Q3', Q4, Q5, Q6, Q7

(c) Solutions: S1

(c) Mid-term: M1, F1

## Preprints

- On fundamental Fourier coefficients of Siegel modular forms. (with S. Böcherer), 39pp.

*(this version proves Andrianov's conjecture on the functional equation of the spinor-function for holomorphic Siegel cusp forms of degree 3, when combined with A. Pollacks's work.)*

- 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).

## Publications

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)

**MR3974676** Das, Soumya; Pal, Ritwik The first negative eigenvalue of Yoshida lifts. *Res. Number Theory* 5 (2019), no. 3, Paper No. 20, 9 pp. (Reviewer: Hideshi Takayanagi) 11F46 (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)

**MR3859224** Das, Soumya; Khan, Rizwanur The third moment of symmetric square L-functions. *Q. J. Math.* 69 (2018), no. 3, 1063–1087. (Reviewer: Valentin Blomer) 11M06

**MR3846155** Böcherer, Siegfried; Das, Soumya Petersson norms of not necessarily cuspidal Jacobi modular forms and applications. *Adv. Math.* 336 (2018), 335–376. (Reviewer: G. K. Sankaran) 11F50 (11F46)

**MR3836146** Böcherer, Siegfried; Das, Soumya Cuspidality and the growth of Fourier coefficients of modular forms. *J. Reine Angew. Math.* 741 (2018), 161–178. (Reviewer: Hideshi Takayanagi) 11F30 (11F46)

**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)

**MR3931445** Anamby, Pramath; Das, Soumya Sturm-like bound for square-free Fourier coefficients. *L-functions and automorphic forms, *1–7, Contrib. Math. Comput. Sci., 10, *Springer, Cham,* 2017. 11F30

**MR3657159** Das, Soumya; Pal, Ritwik Jacobi forms and differential operators: odd weights. *J. Number Theory* 179 (2017), 113–125. (Reviewer: Karam Deo Shankhadhar) 11F50 (11F11 11F25)

**MR3489079** Böcherer, Siegfried; Das, Soumya Cuspidality and the growth of Fourier coefficients: small weights. *Math. Z.* 283 (2016), no. 1-2, 539–553. (Reviewer: Martin Raum) 11F30 (11F46)

**MR3477807** Das, Soumya Cuspidality and the growth of Fourier coefficients of modular forms: a survey. *Indian J. Pure Appl. Math.* 47 (2016), no. 1, 9–22. (Reviewer: Kalyan Chakraborty) 11F30

**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)

**MR3366849** Das, Soumya; Kohnen, Winfried Nonvanishing of Koecher-Maass series attached to Siegel cusp forms. *Adv. Math.* 281 (2015), 624–669. (Reviewer: Valentin Blomer) 11F30 (11F46)

**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)**

**MR3327845** Das, Soumya; Meher, Jaban On quasimodular eigenforms. *Int. J. Number Theory* 11 (2015), no. 3, 835–842. (Reviewer: Dominic A. Lanphier) 11F30 (11F11)

**MR3296015** Das, Soumya; Ramakrishnan, B. Jacobi forms and differential operators. *J. Number Theory* 149 (2015), 351–367. (Reviewer: John Francis Robert Duncan) 11F50 (11F11 11F25)

**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)

**MR3251716** Das, Soumya; Ganguly, Satadal Gaps between nonzero Fourier coefficients of cusp forms. *Proc. Amer. Math. Soc.* 142 (2014), no. 11, 3747–3755. (Reviewer: Scott Ahlgren) 11F30 (11F11 11N25)

**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)

**MR3148511** Das, Soumya; Sengupta, Jyoti An Omega-result for Saito-Kurokawa lifts. *Proc. Amer. Math. Soc.* 142 (2014), no. 3, 761–764. (Reviewer: B. Ramakrishnan) 11F46 (11F30)

**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)

**MR2997487** Das, Soumya On the natural densities of eigenvalues of a Siegel cusp form of degree 2. *Int. J. Number Theory* 9 (2013), no. 1, 9–15. (Reviewer: Suzanne Caulk) 11F46 (11F30)

**MR2997486** Das, Soumya; Ganguly, Satadal Nonvanishing of Poincaré series on average. *Int. J. Number Theory* 9 (2013), no. 1, 1–8. (Reviewer: Barış Kendirli) 11F11 (11F30)

**MR2997572** Das, Soumya; Kohnen, Winfried; Sengupta, Jyoti Nonvanishing of Siegel-Poincaré series II. *Acta Arith.* 156 (2012), no. 1, 75–81. (Reviewer: Ellen E. Eischen) 11F46 (11F30)

**MR2995143** Das, Soumya; Sengupta, Jyoti Nonvanishing of Siegel Poincaré series. *Math. Z.* 272 (2012), no. 3-4, 869–883. (Reviewer: Ellen E. Eischen) 11F46 (11L05)

**MR2975157** Das, Soumya; Ganguly, Satadal Linear relations among Poincaré series. *Bull. Lond. Math. Soc.* 44 (2012), no. 5, 988–1000. (Reviewer: SoYoung Choi) 11F11 (11F30)

**MR2769134** Das, Soumya Nonvanishing of Jacobi Poincaré series. *J. Aust. Math. Soc.* 89 (2010), no. 2, 165–179. (Reviewer: Olav K. Richter) 11F50 (11F30)

**MR2738862** Das, Soumya Some aspects of Hermitian Jacobi forms. *Arch. Math. (Basel)* 95 (2010), no. 5, 423–437. (Reviewer: Anton Deitmar) 11F50 (11F60)

**MR2723724** Das, Soumya Note on Hermitian Jacobi forms. *Tsukuba J. Math.* 34 (2010), no. 1, 59–78. (Reviewer: B. Ramakrishnan) 11F50 (11F55)