NISER

• Ph. D., 2008, Harish-Chandra Research Institute, Allahabad
• M. Sc. (Mathematics), 2001, Sambalpur University, Burla, Sambalpur
• B. Sc. (Mathematics Honors), 1999, Gangadhar Meher College, Sambalpur
• Higher Secondary (+2 Sc.), 1996, Gangadhar Meher College, Sambalpur
• Secondary (10th), 1994, IG High School, Jharanipali

Number Theory

• Science Foundation of Ireland (SFI) Post Doctoral Fellowship 2008-2010
• National Board for Higher Mathematics (NBHM) Doctoral Fellowship 2001
• National Scholarship (1999-2001) for Post Graduate Study, Sambalpur University

1. L-function associated to Jacobi forms of half-integral weight and a converse theorem (with Abhash Kumar Jha, Shivansh Pandey), Journal of Mathematical Analysis and Applications, 534 (2024), no. 1,  paper number. 128041
2. Explicit evaluation of triple convolution sums of the divisor functions (with B. Ramakrishnan and Anup Kumar Singh), Accepted in International Journal Number Theory
3. A simple extension of Ramanujan-Serre derivative map and some applications (with B. Ramakrishnan and Anup Kumar Singh), The Ramanujan Journal, 61 (2023), 1379-1410
4. Representations of squares by certain diagonal quadratic forms in odd number of variables (with B. Ramakrishnan and Anup Kumar Singh), Rocky Mountain Journal of Mathematics, 53 (2023), no. 4,  1219-1244
5. Nonvanishing of kernel functions and Poincare series for Jacobi forms, (with Shivansh Pandey) Journal of Mathematical Analysis and Applications, 515 (2022), no. 2,  paper number. 126455
6. On the number of representations of a natural number by certain quaternary quadratic forms, (with B. Ramakrishnan and Anup Kumar Singh), Modular Forms and Related Topics in Number Theory, Springer Proceedings in Mathematics and Statistics, vol 340, pp: 173-198, 2020
7. Rankin-Cohen type operators for Hilbert-Jacobi forms (with Moni Kumari), Modular Forms and Related Topics in Number Theory, Springer Proceedings in Mathematics and Statistics, vol 340, pp: 143-156, 2020
8. Rankin-Cohen brackets on Jacobi forms of several variables and special values of certain Dirichlet series (with Abhash Kumar Jha),  International Journal Number Theory (15), 2019, no-5, 925-933
9. On the number of representations by certain quadratic forms in 8 variables (with B. Ramakrishnan and Anup Kumar Singh), Automorphic Forms and Related Topics,  215-224, Contemp. Math., Vol-732, American Mathematical Society, Providence, RI, 2019
10. Differential operators on Jacobi forms and special values of certain Dirichlet series (with Abhash Kumar Jha), Automorphic Forms and Related Topics, 91-99, Contemp. Math.,  Vol-732, American Mathematical Society, Providence, RI, 2019
11. Rankin-Cohen brackets on Hilbert modular forms and special values of certain Dirichlet series (with Moni Kumari), Functiones et Approximatio Commentarii Mathematici, 58 (2018), 2, 257-268
12. On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function (with B. Ramakrishnan and Anup Kumar Singh), Functiones et Approximatio Commentarii Mathematici, 58 (2018), 2, 233-244
13. Representations of an integer by some quaternary and octonary quadratic forms, (with B. Ramakrishnan and Anup Kumar Singh), In: Akbary, Amir, Gun, Sanoli (eds.) Geometry, Algebra, Number Theory and Their Information Technology Applications, Springer Proceedings in Mathematics and Statistics, vol 251, pp: 383-409, 2018
14. On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6 (with B. Ramakrishnan and Anup Kumar Singh), International Journal Number Theory, 14 (2018), 3, 751- 812
15. On the representations of a positive integer by ceratin classes of quadratic forms in eight variables (with B. Ramakrishnan and Anup Kumar Singh), In: Andrews G., Garvan F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Springer Proceedings in Mathematics & Statistics,  vol 221. Springer, Cham, pp 641-664, 2017
16. Rankin-Cohen brackets on Siegel modular forms and Special values of Certain Dirichlet series (with Abhash Kumar Jha), The Ramanujan Journal, 44 (2017), 1, 63-73 
17. Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12 (with B. Ramakrishnan), Mathematical Journal of Okayama University, 59 (2017), 71-79
18. On the number of representations of certain quadratic forms in 20 and 24 variables (with B. Ramakrishnan), Functiones et Approximatio Commentarii Mathematici, 54 (2016), 2, 151-161 
19. Identities for the Ramanujan Tau function and certain convolution sum identities for the divisor functions (with B. Ramakrishnan) Number Theory, RMS-Lecture Notes Series, No. 23, 2016, 63-75 
20. Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12 (with B. Ramakrishnan) accepted for publication in Math. J. Okayama Univ.
21. Rankin-Cohen brackets on Jacobi Forms and the adjoint of some linear maps (with Abhash Kumar Jha) accepted for publication in The Ramanujan Journal 
22. Supercongruences for sporadic sequences (with R. Osburn, A. Straub), accepted for publication in Proc. Edinb. Math. Soc. 
23. On the number of representations of certain quadratic forms of sixteen variables Int. J. Number Theory, 10 (2014), 8, 1929-1937(with B. Ramakrishnan), 
24. A supercongruence for generalized Domb numbers, Funct. Approx. Comment. Math.,  48 (2013),  1, 29-36 (with R. Osburn)
25. Evaluation of the convolution sums ∑_{l+15m=n} σ(l)σ(m) and ∑_{3l+5m=n}σ(l)σ(m) and an application, Int. J. Number Theory, 9 (2013), 3, 799-809 (with B. Ramakrishnan)
26. Supercongruences for Apéry-like numbers, Advances in Applied Mathematics, 47 (2011), 631-638 (with R. Osburn)
27. Congruences via modular forms, Proc. Amer. Math. Soc., 139 (2011), 7, 2375-2381 (with R. Osburn)
28. Rankin's method and Jacobi forms of several variables,  Journal of the Australian Math. Soc.,  88 (2010), 1,  131-143 (with B. Ramakrishnan)
29. Distribution of Residues Modulo p, Acta Arith. 129 (2007), 325-333 (with S. Gun, Florian Luca, P. Rath, R. Thangadurai)
30. On the Fourier expansions of Jacobi forms of half integral weight, Int. J. Math. Math. Sci. Vol 2006 (with B. Ramakrishnan)
31. Distribution of quadratic non-residues which are not primitive roots, Math. Bohemica, 130 (2005),  4, 387-396 (with S. Gun, R.Thangadurai, B. Ramakrishnan)

Supercongruences:  The numbers which occur in Ap\'{e}ry's  proof of the irrationality of  zeta(2) and zeta(3)  have many interesting congruence properties.Work started with F.Beukers and D. Zagier,  then extended by G. Almkvist, W. Zudilin and S. Cooper recently has complemented the Ap\'{e}ry numbers with set of sequences know as Ap\'{e}ry-like numbers which share many of the remarkable properties of the Ap\'{e}ry numbers. We study supercongruences properties  of Ap\'{e}ry-like numbers. 

Differential Operators: There are many interesting connections between differential operates and modular forms. Using Rankin-Cohen type differential operators on Jacobi forms/ Siegel modular forms we study certain arithmetic of Fourier coefficients. 

Convolution sums and applications: We compute convolution sums of divisor function using the theory of modular forms and quasi modular forms and apply those to find number of representations of an integer by certain quadratic forms. 

Representations of numbers by quadartic forms: We find number of representations of an integer by certain quadratic forms by computing modular forms/ theta series.

1. Shivansh Pandey (PhD--)
2. Raveena Ganash (PhD--)
3. Gargi Mukherjee (PDF--)
4. Ayanava Mandal (MSc--)

Current Teaching: M463: Finite fields, Fall 2024

1. M463: Finite Fields: Fall 2024, Spring 2022, Fall 2021, Fall 2018, Fall 2017
2. MA601: Algebra I (Graduate): Fall 2023, Fall 2019, Fall 2015, Fall 2013, Fall 2012, Fall 2011
3. M305/MA703: Number Theory: Fall 2022
4. MA605: Topology I (Graduate): Spring 2022
5. M308: Complex Analysis: Spring 2021
6. M403: Commutative Algebra: Fall 2020, Fall 2012, Spring 2011
7. M553: Classical Groups: Spring 2020
8. M101: Mathematics I: Summer 2019, Fall 2016, Summer 2016
9. MTH302: Rings and Modules: Spring 2019 (IISER, Berhampur)
10. M402: Representations of Finite Groups: Spring 2024, Spring 2019, Spring 2018
11. M102: Mathematics II: Summer 2018
12. M205: Linear Algebra: Spring 2017
13. M458: Algebraic Number Theory: Spring 2016
14. M560: Modular forms of one variable: Spring 2015
15. M302: Algebra III: Fall 2014, 
16. M307: Algebra IV: Spring 2014, Spring 2013 
17. M459: Algebraic Topology: Spring 2012
18. M202: Algebra I: Fall 2011
19. M501: Topology: Fall 2010
20. MATH20160: Polynomial Ring and Group Theory: Spring 2009 (UCD)

• Chairperson, School of Mathematical Sciences (July 2022--)
• Member, Board of Studies (Mathematical Sciences), HBNI (2021--)
• Chief Warden (2018-2020)
• Member, Institute Library Committee (2012-2020)