Research Interests
Analytic number theory
Automorphic forms of various types: Maass forms, Hilbert modular forms, Jacobi forms, Siegel modular forms
Automorphic representations
Algebraic Number Theory
Welcome to my Homepage!
I am an assistant professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Jammu. I was at IIT Jodhpur as an Assistant Professor from Sep 2022 (presently on lien).
From August 2020 to July 2022, I was a postdoctoral fellow at Bar-Ilan University, Israel under the supervision of Prof. Andre Reznikov.
Before that, I was a visiting fellow at the Tata Institute of Fundamental Research (TIFR), Mumbai from August 2018 to July 2020.
I did my Ph. D. from NISER, Bhubaneswar under the supervision of Prof. Brundaban Sahu in 2018.
Email: monimath1990@gmail.com, moni.kumari@iitjammu.ac.in
For my MathSciNet page, please click here.
Submitted
(with A. Kumar and A. Weiss) On the Lang-Trotter conjecture for Siegel modular forms.
Publications
(with A. Kumar) Divisors of Fourier coefficients of two newforms, accepted in Pacific Journal of Math.
Comparing Hecke eigenvalues of Siegel eigenforms, Forum Math. 35(1), 2023, 83–93.
(with A. Kumar, P. Moree and S. K. Singh) Ramanujan-style congruences for prime level, Math. Zeitschrift, 303, 19, 2023.
(with J. Sengupta) The quantitative distribution of Hecke eigenvalues of Maass forms, Res. Number Theory 8 (2022), no. 3, Paper No. 49, 18 pp.
(with S. Ganguly and A. Kumar) Coprimality of Fourier coefficients of eigenforms, Acta Arith. 203 (2022), no. 1, 69-96.
(with Y. Kara, J. Marzec, K. Maurischat, A. Mocanu and L. Smajlovic) Construction of Poincare-type series by generating kernels, Women in numbers Europe III—research directions in number theory, 233–274, Assoc. women Math. Ser., 24, Springer, Cham, (2021).
(with J. Sengupta), The first simultaneous sign change of Fourier coefficient of Maass forms, Ramanujan Journal, 55 (2021), 205–218.
(with B. Sahu), Rankin-Cohen type operators for Hilbert-Jacobi forms, Modular Forms and Related Topics in Number Theory, 143–156, Springer Proceedings in Mathematics and Statistics, Vol. 340, 2020.
(with S. Kumar Singh) On the parity of Fourier coefficients of hauptomoduln j_N(z) and j_N^{+}(z), Acta Arith. 188 (2019), no. 2, 171-182.
Non-vanishing of Hilbert Poincare series, J. Math. Anal. Appl. 446 (2018), 1476-1485.
(with B. Sahu) Rankin-Cohen brackets on Hilbert Modular forms and special values of certain Dirichlet series, Funct. Approx. Comment. Math. 58 (2018), no. 2, 257-268.
(with M. Ram Murty) Simultaneous non-vanishing and sign changes of Fourier coefficients of Modular forms, Int. J. Number theory, 14, no. 8 (2018), 257-268.
Teaching
Teaching at IIT Jodhpur
August-September, 2023: Matrix Theory (M. Tech.).
January-April, 2023: MAL6310: Measure and Integration (M. Sc. elective).
Teaching at NISER, Bhubaneswar:
Annual Foundation School III (Functional Analysis), July 1-27, 2019 (TA).
M101: Mathematics I, General Mathematics, Fall, 2016 (TA).
M101: Mathematics I, General Mathematics, Fall, 2015 (TA).
M101: Mathematics II, Real Analysis, Spring, 2014 (TA).
Talks
Comparing Hecke eigenvalues of Siegel eigenforms, Number theory conference, NISER, Bhubaneswar, 25 February, 2023.
Divisors of Fourier coefficients of two newforms, Number Theory lunch seminar, MPIM, Bonn, Germany, 14 September, 2022.
Ramanujan-style congruences for prime level, Algebra seminar (online), Bar-Ilan University, Israel, 30 March 2022.
Ramanujan-style congruences for prime level, Number theory lunch seminar (online), MPIM, Bonn, Germany, 2 Feb 2022.
Non-vanishing of Hilbert-Poincare series, International (online) Seminar on Automorphic Forms, TU-Darmstadt, Germany, 4 May 2021.
Construction of Poincare-type series by generating kernels, International conference on number theory and algebra, IIT BHU (online), Varanasi, 22 Dec 2020.
Modular forms and the parity of j-function, Colloquium, RKMVERI, Kolkata, India, 25 Sep 2019.
Non-vanishing of Hilbert Poincare series, Colloquium, TIFR, Mumbai, India, 09 May 2019.
Non-vanishing of Hilbert Poincare series, Colloquium, ISI, Kolkata, India. 08 April 2019.
Distribution of Fourier coefficients of a Hecke-Maass form, Annual meeting, TIFR, Mumbai, India, 07 Jan 2019.
Rankin-Cohen type operators for Hilbert-Jacobi forms, Workshop in number theory, NISER, Bhubaneswar, India, 02 Dec 2018.
Non-vanishing of Hilbert-Poincare series, Workshop in modular forms, KSOM, Kerala, India, 14 Oct 2018.
Rankin-Cohen type operators for Hilbert-Jacobi forms, School on modular forms, KSOM, Kerala, India, 22 Feb 2018.
Non-vanishing of Hilbert-Poincare series, Number theory: Arithmetic, Diophantine and Transcendence, IIT Ropar, India, 22 Dec 2017.
Simultaneous non-vanishing and sign changes of Fourier coefficients of Modular forms, Cimpa School, Nesin mathematics village, Sirince, Turkey, 8 June 2017.
Euler's famous prime generating polynomial, NISER, India, 2014.
Dirichlet unit theorem, NISER, India, 2014.
Cubic and Biquadratic reciprocity law, NISER, India, 2013.
Academic activities
AMS Reviewer
Reviewer for journals: Research in Number Theory, The Ramanujan Journal, The Rocky Mountain Journal of Mathematics, Indian Journal of Pure and Applied Mathematics.
SPS Committee (IIT Jodhpur)-Sep 5, 2023-Feb2024.
DFB Convenor (IIT Jodhpur)-Jan 4, 2023-Sep 5, 2023.
Past events
National Mathematics Day (December 22, 2022), IIT Jodhpur.
Schools/ Conferences attended
Women in Numbers Europe 3, Centre de la Hublais, Rennes, France, 26-30, Aug 2019.
NSF-CBMS Conference: L-functions and Multiplicative Number Theory, University of Mississippi, USA, 20-24, May 2019.
Algebraic and Analytic Aspects of Automorphic Forms}, ICTS, Banglore, India, 25 Feb-07 March 2019
5th Mumbai-Pune number theory seminar}, IISER Pune, 15 - 16 Feb 2019.
Conference in number theory, KSOM, Kerala, India, 10-14 Dec 2018.
Workshop in number theory, NISER, Bhubaneswar, India, 30 Nov- 06 Dec 2018.
Workshop in modular forms, KSOM Kerala, India, 12-14 Oct 2018.
L-functions, IIT Mumbai, 25-30 June 2018.
School on modular forms, KSOM, Kerala, 12-24 Feb 2018.
Analytic number theory, ATM workshop, ISI, Kolkata, 26-30 Dec 2017.
Number Theory: Arithmetic, Diophantine and Transcedenence, celebrating 130-th birth anniversary of S. Ramanujan, IIT Ropar, Rupnagar, 22-25 Dec 2017.
Transcendental Numbers and Special Values of Dirichlet Series, IIT Ropar, Rupnagar, 16-21 Dec 2017.
Siegel modular forms and associated representations, By Prof. Ameya Pitale, GIAN course, IISER Pune, 07-18 Aug 2017
Artin L-functions, Artin's primitive roots conjecture and applications, Nesin mathematics village, Sirince, Turkey, 29 May-09 June 2017
School and Workshop on Modular Forms and Black Holes, NISER, Bhubaneswar, 05-14 Jan 2017.
Discussion Meeting on Automorphic forms, NISER, Bhubaneswar, 21-27 Dec 2016.
Two days Number Theory Meet, HRI, Allahabad, 06-07 Sept 2016.
Conference on Modular Forms, IISER, Bhopal, 04 Sep 2016.
A Short Course on Modular Forms, IISER, Bhopal, 24 Aug-03 Sep 2016.
Number Theory Conference on Arithmetic Geometry and L-Functions, In honour of Prof. V. Kumar Murty, KSOM, Kozhikode, 17-21 Aug 2016.
Automorphic Forms on Metaplectic Groups and Related Topics, IISER Pune, Pune, 04-09 July 2016.
AIS-Analytic Theory of Algebraic Numbers, KIIT, Bhubaneswar, 13 Jun-02 July 2016.
Workshop on Automorphic Forms, KSOM, Kozhikode, 10-16 Feb 2016.
AFS-III, HRI, Allahabad, 29 Jun-25 July 2015.
International Conference on Automorphic Forms and Applications, KSOM, Kozhikode, 13-14 Feb 2015.
Workshop on Jacobi Forms and Modular Forms, KSOM, Kozhikode, 02-12 Feb 2015.
AIS-Analytic Number Theory, KIIT, Bhubaneswar, 01-20 Jun 2015.
Winter School on Modular Functions in One and Several Variables, Goa University, Goa. 08-17 Dec 2014.
AIS- Algebraic Number Theory, CMI, Chennai, 07-26 July 2014.
AFS-II, CEMS, Almora, 01 May-28 May 2014.
AFS-I, KSOM, Kozhikode, 02-28 Dec 2013.
Academic visits
SRM University, AP, India. 10-15 July 2023.
Max Planck Institute for Mathematics (MPIM), Bonn, Germany. 05 Aug-29 Sept 2022.
Ramakrishna Mission Vivekananda Educational and Research Institute (RKMVERI), Belur Math, Howrah, India. 23-30 Sep 2019.
Indian Statical Institute, Kolkata, India. 01-11 April 2019.
Tata Institute of Fundamental Research (TIFR), Mumbai, India, 02-08 April 2018.
Kerala School of Mathematics (KSOM), Kozhikode, India, 04-17 Dec 2016.