Welcome to my homepage

Soumya Das

Assistant 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: Uddalok (1st year), Sarbartha (1st year), Agneedh Basu (2nd year), Subham Pandey (1st year), Ankit Roy (1st year)

Summer students (2018):

Ananth Subray P V, Anjali G, Banashree B S, Kruthika H H (Christ University).

Suparna Mondal, Rohit Kumar, Debabrata Ghosh, Shubham Pandey, Sarbartha, Aaradhya, Gokul (UG) → ∞

Teaching

Jan 2018: (i) UM203: 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's are Samarpita Ray and Surjadipta De Sarkar.

* The mid semestral examination has been scheduled on 17 February from 2 PM onwards, the venue being the class. Lets keep it an exam of at most 3 hour duration, and 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 21 April, from 2PM onwards. Venue would be F12 in Old Physics building. 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, P5, P6

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

(ii) MA218: Number Theory: Pretentious viewpoint of number theory, sieves etc. à la Soundararajan, Granville..

Publications

  1. Note on Hermitian Jacobi forms. Tsukuba Journal of Mathematics, 34 no.1, (2010), 59–78. PDF
  2. Some aspects of Hermitian Jacobi forms. Archiv der Mathematik, 95 no.5, (2010), 423–437. PDF
  3. Nonvanishing of Jacobi Poincaré series. J. Aust. Math. Soc., 89 no. 2, (2010), 165–179. PDF
  4. Nonvanishing of Siegel Poincaré series. Math. Z., 272 no. 3-4, (2012), 869–883. (With J. Sengupta) PDF
  5. Linear relations among Poincaré series. Bull. London Math. Soc., 44. no. 5, 2012, 988–1000. (With S. Ganguly) PDF
  6. Nonvanishing of Siegel Poincaré series II. Acta Arith., 156 no.1, 2012, 75–81. (With W. Kohnen and J. Sengupta) PDF
  7. On holomorphic differential operators equivariant for the inclusion of Sp(n, R) in U(n, n). International Mathematics Research Notices (IMRN), 2013, No. 11, 2534–2567. (With S. Böcherer) PDF
  8. Omega result for Saito–Kurokawa lifts. Proc. Amer. Math. Soc., Volume 142, Number 3, March 2014, Pages 761–764. (With J. Sengupta) PDF
  9. Nonvanishing of Poincaré series on average. Int. J. Number Theory (IJNT), 9, no. 1, (2013), 1–8. (With S. Ganguly) PDF
  10. On the natural densities of eigenvalues of a Siegel cusp form of degree 2. Int. J. Number Theory (IJNT), 9, no. 1, (2013), 9–15. PDF
  11. Gaps between nonzero Fourier coefficients of cusp forms. Proc. Amer. Math. Soc., 142, (2014), 3747-3755. (With S. Ganguly) PDF
  12. Lnorms of holomorphic modular forms in the case of compact quotient. Forum Math., 27 (issue 4), 1987-2001. (With J. Sengupta) PDF
  13. Characterisation of Siegel cusp forms by the growth of their Fourier coefficients. Math. Ann., 358, Issue 1, (2014), 169-188. (With S. Böcherer) PDF
  14. Linear independence of Poincaré series of exponential type via non-analytic methods. Trans. of Amer. Math. Soc., 367 (2015), 1329-1345. (With S. Böcherer) PDF
  15. On a convolution series attached to a Siegel Hecke cusp form of degree 2. Ramanujan J., 33, issue 3, (2014), 367-378. (With W. Kohnen and J. Sengupta) PDF
  16. Some remarks on the Resnikoff-Saldaña conjecture. Proceedings of the ’Legacy of Ramanujan’ conference, RMS Lecture Notes, Vol. 20, 153-161. (With W. Kohnen) PDF
  17. On the growth of Fourier coefficients of Siegel modular forms. RIMS Kokyuroku 1871, Kyoto Univ., 2013-12, 136-144. (With S. Böcherer) PDF
  18. Jacobi forms and differential operators. J. Number Theory, 149 (2015), 351-367. (With B. Ramakrishnan) PDF
  19. On Quasimodular eigenforms. Int. J. Number Theory, 11, no. 3, (2015), 835-842. (With J. Meher) PDF
  20. Nonvanishing of the Koecher-Maass series attachted to Siegel cusp forms. Adv. Math., 281 (2015), 624-669. (With W. Kohnen) PDF
  21. Cuspidality and the growth of Fourier coefficients of modular forms. J. Reine Angew. Math., vol. 2018, issue 741 (2018), 161-178. (With S. Böcherer) PDF
  22. A note on small gaps between nonzero Fourier coefficients of cusp forms. Proc. Amer. Math. Soc., 144, No. 6, June 2016, Pages 2301–2305. (With S. Ganguly) PDF
  23. Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions. J. Ramanujan Math. Soc., 30, no. 3, (2015), 237-250. (With R. Khan) PDF
  24. Cuspidality and the growth of Fourier coefficients: Small weights. Math. Z., 283, Issue 1, pp 539-553. (With S. Böcherer) PDF
  25. Growth of Fourier coefficients of modular forms and cuspidality, a survey. Indian J. Pure and Appl. Math., 47, Issue 1, pp 9-22. PDF
  26. Jacobi forms and differential operators: odd weights. J. Number Theory, Volume 179, October 2017, Pages 113–125. (With R. Pal) PDF
  27. On sign changes of eigenvalues of Siegel cusp forms of genus 2 in prime powers. Acta Arith. 183 (2018), pp 167–172. (With W. Kohnen) PDF
  28. Sturm-like bound for square-free Fourier coefficients. Proceedings of the Conference ”L-functions and Automorphic Forms” at Heidelberg 2016, (With P. Anamby) PDF
  29. Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients. Publ. Mat., to appear 2018, 32pp. (With P. Anamby) PDF
  30. On sign changes of eigenvalues of Siegel cusp forms of genus 2 in prime powers. Acta Arith. 183 (2018), pp 167–172. (With W. Kohnen) PDF
  31. The third moment of symmetric-square L-functions. Q. J. Math., appeared online https://doi.org/10.1093/qmath/hay012. (With R. Khan) PDF
  32. Bounds for the Petersson norms of the pullbacks of Saito-Kurokawa lifts. J. Number Theory, 191, (2018), 289-304 (With P. Anamby) PDF
  33. 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, to appear. (With P. Anamby) PDF
  34. Petersson norms of not necessarily cuspidal Jacobi modular forms and applications. Adv. Math., 336, (2018), 336-375. (with S. Böcherer) PDF

Preprints

  1. On fundamental Fourier coefficients of Siegel modular forms. (submitted, 28 pp., with S. Böcherer) PDF
  2. Sup-norm bounds for Jacobi forms of index 1 and for Saito-Kurokawa lifts. (submitted, intended for the conference proceedings at IIT ROPAR, with J. Sengupta) PDF
  3. Analytic properties of twisted real-analytic Hermitian Klingen-type Eisenstein series and applications. (submitted, 13pp., with A. K. Jha) PDF
  4. The first negative eigenvalue of Yoshida lifts. (submitted, 11pp., with R. Pal) PDF