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 and Preprints

  1. Note on Hermitian Jacobi forms. Tsukuba J. Math., 34 no.1, (2010), 59-78.(PDF)
  2. Some aspects of Hermitian Jacobi forms. Arch. Math. (Basel), 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. (With Jyoti Sengupta) Math. Z., 272 no. 3-4, 2012, 869-883. (PDF)
  5. Linear relations among Poincaré series. (With Satadal Ganguly) Bull. London Math. Soc., 44, no. 5, (2012) 988-1000. (PDF)
  6. Nonvanishing of Siegel Poincaré series II. (With Winfried Kohnen and Jyoti Sengupta) Acta Arith., 156, no. 1, (2012) 75-81. (PDF)
  7. On holomorphic differential operators equivariant for the inclusion of Sp(n,R) in U(n,n). (With Siegfried Boecherer) Int. Math. Res. Not. (IMRN), Vol. 2013, No. 11, 2534-2567. (PDF)
  8. Omega result for Saito--Kurokawa lifts. (With Jyoti Sengupta) Proc. Amer. Math. Soc., 142, (2014), 761-764. (PDF).
  9. Nonvanishing of Poincaré series on average. (With Satadal Ganguly) Int. J. Number Theory, 09, No. 01 (2013) 1-8. (PDF)
  10. On the natural densities of eigenvalues of a Siegel cusp form of degree 2. Int. J. Number Theory (IJNT), 09, no. 1, (2013) 9-15. (PDF)
  11. Gaps between non-zero Fourier coefficients of cusp forms. (With Satadal Ganguly) Proc. Amer. Math. Soc, 142, (2014), 3747--3755. (PDF)
  12. L norms of holomorphic modular forms in the case of compact quotient. (With Jyoti Sengupta) Forum Math., 27 (issue 4), 1987-2001. (PDF)
  13. Characterization of Siegel cusp forms by the growth of their Fourier coefficients. (With Siegfried Boecherer) Math. Ann., 358, Issue 1, (2014), 169--188. (PDF)
  14. On a convolution series attached to a Siegel Hecke cusp form of degree 2. (With Winfried Kohnen and Jyoti Sengupta) Ramanujan J., 33, issue 3, (2014), 367--378. (PDF)
  15. Linear independence of Poincaré series of exponential type via non-analytic methods. (With Siegfried Boecherer) Trans. Amer. Math. Soc., 367 (2015), 1329-1345. (PDF)
  16. Some remarks on the Resnikoff-Saldana conjecture. (With W. Kohnen) Proceedings of the 'Legacy of Ramanujan' conference, RMS Lecture Notes, Vol. 20, 153-161. (PDF)
  17. On the growth of Fourier coefficients of Siegel modular forms. (With Siegfried Boecherer) RIMS Kokyuroku 1871, Kyoto Univ., 2013-12, 136-144. (PDF)
  18. On Quasimodular eigenforms. (With J. Meher) Int. J. Number Theory, 11, no. 3, (2015), 835-842. (PDF)
  19. Jacobi forms and Differential operators. (With B. Ramakrishnan) J. Number Theory, 149 (2015), 351-367. (PDF)
  20. Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions. (With R. Khan) J. Ramanujan Math. Soc., 30, no. 3, (2015), 237-250. (PDF)
  21. Nonvanishing of the Koecher-Maass series attached to Siegel cusp forms. (With W. Kohnen) Adv. Math., 281 (2015), 624-669. (PDF)
  22. A note on small gaps between nonzero Fourier coefficients of cusp forms. (With S. Ganguly) Proc. Amer. Math. Soc., Volume 144, Number 6, June 2016, Pages 2301–2305. (PDF)
  23. Cuspidality and the growth of Fourier coefficients of Modular forms. (With S. Boecherer) J. reine angew. Math., DOI 10.1515/ crelle-2015-0075.(PDF)
  24. Cuspidality and the growth of Fourier coefficients: Small weights. (With S. Boecherer) Math. Z., June 2016, Volume 283, Issue 1, pp 539-553. (PDF)
  25. Jacobi Forms and Differential Operators: odd weights. (With R. Pal) J. Number Theory, 179, (2017) 113-125. (PDF)
  26. Sturm-like bound for square-free Fourier coefficients. (With P. Anamby) Proc. of the conference "L-functions and Automorphic forms" at Univ. Heidelberg 2016, (publ. Springer), to appear. (PDF)
  27. Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients. (With P. Anamby) Publicacions Matemàtiques, to appear. (PDF) (final version)
  28. On sign changes of eigenvalues of Siegel cusp forms of genus 2 in prime powers. (With. W. Kohnen) Acta Arith, 183 (2018), pp 167--172. (PDF)
  29. The third moment of symmetric-square L-functions. (With R. Khan) Q. J. Math, appeared online https://doi.org/10.1093/qmath/hay012. (PDF)
  30. Bounds for the Petersson norms of the pullbacks of Saito-Kurokawa lifts. (With P. Anamby) J. Number Theory, appeared online, https://doi.org/10.1016/j.jnt.2018.03.011. (PDF)
  31. Hecke-Siegel type threshold for square-free Fourier coefficients: an inprovement. (With P. Anamby), RIMS Kokyuroku Kyoto Univ., proceedings for the conference “Analytic and Arithmetic Theory of Automorphic Forms”, January 2018, to appear. (PDF)
  32. Petersson norms of not necessarily cuspidal Jacobi modular forms and applications. (With S. Boecherer) Adv. Math., 336, (2018), 336-375. (PDF)

Preprints

  1. Analytic properties of twisted real-analytic Hermitian Klingen-type Eisenstein series and applications. (With A. K. Jha) (PDF)
  2. The first negative eigenvalue of Yoshida lifts. (With R. Pal) (PDF)

Other

  1. Growth of Fourier coefficients of modular forms and cuspidality, a survey. Indian J. Pure and Appl. Math., March 2016, Volume 47, Issue 1, pp 9-22.