+91-674-249-4082

Submitted by brundaban.sahu on 15 July, 2014 - 10:57

Designation:

Reader-F

Research Area:

Number Theory

Education:

**Ph. D., 2008, Harish-Chandra Research Institute**

**M. Sc., 2001, Sambalpur University**

**B. Sc., 1999, Gangadhar Meher College**

Research Interest:

**Specialisation: Number Theory, Modular Forms **

**Present Research Interests:**

** 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.

Publications:

- Rankin-Cohen brackets on Hilbert modular forms and special values of certain Dirichlet series (with Moni Kumari), Accepted in Functiones et Approximatio Commentarii Mathematici

- On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function (with B. Ramakrishnan and Anup Kumar Singh) Accepted in Functiones et Approximatio Commentarii Mathematici

- Representations of an integer by some quaternary and octonary quadratic forms, (with B. Ramakrishnan and Anup Kumar Singh) Accepted in Geometry, Algebra, Number Theory and Their Information Technology Applications (GANITA) in honor of Professor V. Kumar Murty, Springer Proceedings in Mathematics and Statistics

- 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), Accepted in
*Int. J. Number Theory*

- On the representations of a positive integer by ceratin classes of quadratic forms in eight variables (with B. Ramakrishnan and Anup Kumar Singh), To appear in Analytic Number Theory, Modular Forms and q-Hypergeometric Series in honor of Professor K. Alladi, Springer Proceedings in Mathematics and Statistics

- Rankin-Cohen brackets on Siegel modular forms and Special values of Certain Dirichlet series (with Abhash Kumar Jha) accepted for publication in
*The Ramanujan Journal*

- On the number of representations of ceratin quadratic forms in 20 and 24 variables,
*Funct. Approx. Comment. Math.,*54 (2016), 2, 151-161 (with B. Ramakrishnan).

- Identities for the Ramanujan Tau function and certain convolution sum identities for the divisor functions, Number Theory,
*Lecture Notes Series in Ramanujan Mathematicial Society, No*. 23, 2016, 63-75 (with B. Ramakrishnan)

- Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12,
*Math. J. Okayama Univ*. 59 (2017), 71-79 (with B. Ramakrishnan)

- Rankin-Cohen brackets on Jacobi Forms and the adjoint of some linear maps,
*The Ramanujan Journal*, 39 (2016), 3, 533-544 (with Abhash Kumar Jha)

- Supercongruences for sporadic sequences,
*Proc. Edinb. Math. Soc.*, 59 (2016), 2, 503-518 (with R. Osburn, A. Straub)

- On the number of representations of certain quadratic forms of sixteen variables
*Int. J. Number Theory*, 10 (2014), 8, 1929-1937(with B. Ramakrishnan),

- A supercongruence for generalized Domb numbers,
*Funct. Approx. Comment. Math*., 48 (2013), 1, 29-36 (with R. Osburn)

- 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)

- Supercongruences for Apéry-like numbers,
*Advances in Applied Mathematics*, 47 (2011), 631-638 (with R. Osburn)

- Congruences via modular forms,
*Proc. Amer. Math. Soc.*, 139 (2011), 7, 2375-2381 (with R. Osburn)

- Rankin's method and Jacobi forms of several variables,
*Journal of the Australian Math. Soc.*, 88 (2010), 1, 131-143 (with B. Ramakrishnan)

- Distribution of Residues Modulo p,
*Acta Arith.*129 (2007), 325-333 (with S. Gun, Florian Luca, P. Rath, R. Thangadurai)

- On the Fourier expansions of Jacobi forms of half integral weight,
*Int. J. Math. Math. Sci.*Vol 2006 (with B. Ramakrishnan)

- Distribution of quadratic non-residues which are not primitive roots,
*Math. Bohemica*, 130 (2005), 4, 387-396 (with S. Gun, R.Thangadurai, B. Ramakrishnan)

Preprints:

- Rankin-Cohen Brackets and van der Pol-Type Identities for the Ramanujan's Tau Function (with B. Ramakrishnan), arXiv:0711.3512v1

Teaching:

M463: Finite Fields

Sponsored Projects:

**Project Title: **Modular Forms and Supercongruences (SR/FTP/MS-053/2012) **Funding Organisation:** Department of Science and Technology, Govt. of India **Amount:** Rs 12,24,000/- **Duration:** 3 Years

Contact:

Office Phone:

249 4098

Office Room:

M215

Office address:

NISER, BHUBANESWAR
VIA- JATNI
KHURDHA-752050
ODISHA

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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