## All Publications

### Total Publications 50

1. Certain quaternary quadratic forms of level 48 and their representation numbers (with Brundaban Sahu and Anup Kumar Singh), submitted for publication 2018.
2. Shimura lifts of certain class of modular forms of half-integral weight (with Manish Kumar Pandey), submitted for publication 2017.
3. On the number of representations of certain quadratic forms in 8 variables (with Brundaban Sahu and Anup Kumar Singh), submitted for publication 2017.
4. Representations of an integer by some quaternary and octonary quadratic forms (with Brundaban Sahu and Anup Kumar Singh), in ”Geometry, Algebra, Number Theory and their Information Technology Applications (GANITA)”, in honor of Prof. V. Kumar Murty, Springer Proc. Math. and Stat. (2018). To appear.
5. On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function (with Brundaban Sahu and Anup Kumar Singh), Funct. Approx. Comment. Math. 58 (2018), no. 2, 233–244.
6. Estimates for Fourier coefficients of Hermitian cusp forms of degree two (with Arvind Kumar), Acta Arith. 183 (2018), no. 3, 257–275.
7. On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6 (with Brundaban Sahu and Anup Kumar Singh), Int. J. Number Theory 14 (2018), no. 3, 751–812.
8. On the representations of a positive integer by certain classes of quadratic forms in eight variables (with Brundaban Sahu and Anup Kumar Singh), Analytic number theory, modular forms and q-hypergeometric series, 641–664, Springer Proc. Math. Stat., 221, Springer, Cham, 2017.
9. Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12 (with Brundaban Sahu), Math. J. Okayama Univ. 59 (2017), [2016 on cover], 71–79.
10. On the number of representations of certain quadratic forms in 20 and 24 variables (with Brundaban Sahu), Funct. Approx. Comment. Math. 54 (2016), no. 2, 151–161.
11. Theory of newforms of half-integral weight (with M Manickam and Jaban Meher). Pacific J. Math. 274 (2015), no. 1, 125–139.
12. Jacobi forms and differential operators (with Soumya Das), J. Number Theory 149 (2015), 351–367.
13. Nonvanishing of L-functions associated to cusp forms of half-integral weight. Automorphic forms (with Karam Deo Shankhadhar), 223–231, Springer Proc. Math. Stat., 115, Springer, Cham, 2014.
14. On the number of representations of an integer by certain quadratic forms in sixteen variables (with Brundaban Sahu), Int. J. Number Theory 10 (2014), no. 8, 1929–1937.
15. On the restriction map for Jacobi forms (with Karam Deo Shankhadhar), Abh. Math. Semin. Univ. Hambg. 83 (2013), no. 2, 163–174.
16. On a correspondence between Jacobi cusp forms and elliptic cusp forms (with Karam Deo Shankhadar), Int. J. Number Theory 9 (2013), no. 4, 917–937.
17. Evaluation of the convolution sums $\sum_{l+15m=n} \sigma(l)\sigma(m)$ and $\sum_{3l+5m=n} \sigma(l)\sigma(m)$ and an application (with Brundaban Sahu), Int. J. Number Theory 9 (2013), no. 3, 799–809.
18. Modular forms of half-integral weight, Expanded version of the 22nd Srinivasa Ramanujan Memorial Award lecture delivered at the 77th Annual Conference of the Indian Mathematical Society held at Swami Ramanand Teerth Marathwada University, Nanded, December 27–30, 2011. Math. Student 81 (2012), no. 1-4, 101–114.
19. The theta-operator and the divisors of modular forms. (with Sanoli Gun), Ramanujan Math. Soc. Lect. Notes Ser., 15, Ramanujan Math. Soc., Mysore, 2011.
20. A note on special values of certain Dirichlet L-functions, Bull. Aust. Math. Soc. 83 (2011), no. 3, 435–438.
21. On the representation of integers as sums of two, three and four squares, Math. Student 79 (2010), no. 1-4, 117–141 (2011).
22. Rankin's method and Jacobi forms of several variables (with Brundaban Sahu), J. Aust. Math. Soc. 88 (2010), no. 1, 131–143.
23. A canonical subspace of modular forms of half-integral weight (with Sanoli Gun, M. Manickam), Math. Ann. 347 (2010), no. 4, 899–916.
24. On the representation of integers as sums of an odd number of squares (with Sanoli Gun), Ramanujan J. 15 (2008), no. 3, 367–376.
25. On special values of certain Dirichlet L-functions (with Sanoli Gun), Ramanujan J. 15 (2008), no. 2, 275–280.
26. On the lacunarity of two-eta-products (with Shaun Cooper and Sanoli Gun), Georgian Math. J. 13 (2006), no. 4, 659–673.
27. On the Fourier expansions of Jacobi forms of half-integral weight (with Brundaban Sahu), Int. J. Math. Math. Sci. 2006, Art. ID 14726, 11 pp.
28. An Eichler-Zagier map for Jacobi forms of half-integral weight (with M. Manickam), Pacific J. Math. 227 (2006), no. 1, 143–150.
29. Relations among Fourier coefficients of certain eta products (with Shaun Cooper, Sanoli Gun and Michael Hirschhorn), Integers 5 (2005), no. 1, A16, 6 pp.
30. Distribution of quadratic non-residues which are not primitive roots (with Sanoli Gun, Brundaban Sahu and R. Thangadurai), Math. Bohem. 130 (2005), no. 4, 387–396.
31. An estimate for a certain average of the special values of character twists of modular L-functions (with M. Manickam), Proc. Amer. Math. Soc. 133 (2005), no. 9, 2515–2517.
32. An introduction to modular forms and Hecke operators. Elliptic curves, modular forms and cryptography (with M. Manickam), (Allahabad, 2000), 2223–245, Hindustan Book Agency, New Delhi, 2003.
33. A note on certain divisibility properties of the Fourier coefficients of normalized Eisenstein series (with R. Thangadurai), Expo. Math. 21 (2003), no. 1, 75–82.
34. On Saito-Kurokawa correspondence of degree two for arbitrary level (with M. Manickam), J. Ramanujan Math. Soc. 17 (2002), no. 3, 149–160.
35. Theory of newforms for the Maaß Spezialschar. Cohomology of arithmetic groups, L-functions and automorphic forms, Tata Inst. Fund. Res. Stud. Math., 15, Tata Inst. Fund. Res., Bombay, 2001.
36. On the Eichler-Zagier map. Number theory and related topics, (Seoul, 1998), 29–52, Yonsei Univ. Inst. Math. Sci., Seoul, 2000.
37. A brief introduction to modular forms. Cyclotomic fields and related topics, (Pune, 1999), 219–238, Bhaskaracharya Pratishthana, Pune, 2000.
38. On Shimura, Shintani and Eichler-Zagier correspondences (with M. Manickam), Trans. Amer. Math. Soc. 352 (2000), no. 6, 2601–2617.
39. On exceptions of integral quadratic forms. Number theory (with A. K. Lal) Number theory (Tiruchirapalli, 1996), 151–170, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998.
40. Modular forms which behave like theta series (with K. Chakraborty and A. K. Lal), Math. Comp. 66 (1997), no. 219, 1169–1183.
41. A note on Jacobi forms of higher degree (with K. Chakraborty and T. C. Vasudevan), Abh. Math. Sem. Univ. Hamburg 65 (1995), 89–93.
42. A note on Hecke eigenforms (with K. Chakraborty), Arch. Math. (Basel) 63 (1994), no. 6, 509–516.
43. Theory of newforms, Bull. Allahabad Math. Soc. 8/9 (1993/94), 69–89 (1997).
44. On Saito-Kurokawa descent for congruence subgroups (with M. Manickam and T. C. Vasudevan), Manuscripta Math. 81 (1993), no. 1-2, 161–182.
45. Addendum: "On the theory of newforms of half-integral weight (with M. Manickam and T. C. Vasudevan), [J. Number Theory 34 (1990), no. 2, 210–224; MR1042494]. J. Number Theory 42 (1992), no. 3, 369–371.
46. On a remark of Atkin-Lehner (with M. Manickam and T. C. Vasudevan), J. Number Theory 40 (1992), no. 2, 251–253.
47. Diagonalising modular forms of half-integral weight (with M. Manickam and T. C. Vasudevan), J. Number Theory 40 (1992), no. 1, 32–37.
48. On the theory of newforms of half-integral weight (with M Manickam and T. C. Vasudevan), J. Number Theory 34 (1990), no. 2, 210–224.
49. On Shintani correspondence (with M. Manickam and T. C. Vasudevan), Proc. Indian Acad. Sci. Math. Sci. 99 (1989), no. 3, 235–247.
50. Hecke operators on modular forms of half-integral weight (with M. Manickam and T. C. Vasudevan), Arch. Math. (Basel) 51 (1988), no. 4, 343–352.