All Publications

Total Publications 42 Courtesy: MatSciNet

  1. Evaluation of convolution sums and some remarks on cusp forms of weight 4 and level 12 Authors: B Ramakrishnan and Brundaban sahu. Math. J. Okayama Univ. 59 (2017), [2016 on cover], 71–79. 11F11 (11A25 11E20 11E25)
  2. On the number of representations of certain quadratic forms in 20 and 24 variables. Authors: B Ramakrishnan and Brundaban sahu. Funct. Approx. Comment. Math. 54 (2016), no. 2, 151–161. (Reviewer: Poo-Sung Park) 11E25 (11A25 11E20 11F11)
  3. Theory of newforms of half-integral weight. Authors: M Manickam, Jaban Meher, B Ramakrishnan. Pacific J. Math. 274 (2015), no. 1, 125–139. (Reviewer: Djordje Milićević) 11F37 (11F11 11F32)
  4. Jacobi forms and differential operators. Authors: Soumya Das and B Ramakrishnan. J. Number Theory 149 (2015), 351–367. (Reviewer: John Francis Robert Duncan) 11F50 (11F11 11F25)
  5. Nonvanishing of L-functions associated to cusp forms of half-integral weight. Automorphic forms. Authors: B Ramakrishnan and Karam Deo Shankhadhar. 223–231, Springer Proc. Math. Stat., 115, Springer, Cham, 2014. (Reviewer: Wen-Wei Li) 11F37 (11F25 11F30 11F66)
  6. On the number of representations of an integer by certain quadratic forms in sixteen variables. Authors: B Ramakrishnan and BrundabanSahu. Int. J. Number Theory 10 (2014), no. 8, 1929–1937. (Reviewer: Bülent Köklüce) 11E25 (11A25 11E20 11F11)
  7. On the restriction map for Jacobi forms. Authors: B Ramakrishnan and Karam Deo Shankhadhar. Abh. Math. Semin. Univ. Hambg. 83 (2013), no. 2, 163–174. (Reviewer: Jaban Meher) 11F50 (11F11)
  8. On a correspondence between Jacobi cusp forms and elliptic cusp forms. Authors: B Ramakrishnan and Karam Deo Shankhadar. Int. J. Number Theory 9 (2013), no. 4, 917–937. (Reviewer: Olav K. Richter) 11F50 (11F11 11F32)
  9. Evaluation of the convolution sums ∑l+15m=nσ(l)σ(m) and ∑3l+5m=nσ(l)σ(m) and an application. Authors: Brundaban Sahu and B Ramakrishnan. Int. J. Number Theory 9 (2013), no. 3, 799–809. (Reviewer: Spencer Hamblen) 11A25 (11E20 11E25 11F11 11F20)
  10. 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. Authors: B Ramakrishnan. Math. Student 81 (2012), no. 1-4, 101–114. 11F37
  11. The theta-operator and the divisors of modular forms. Authors: Sanoli Gun and B Ramakrishnan. Ramanujan Math. Soc. Lect. Notes Ser., 15, Ramanujan Math. Soc., Mysore, 2011. (Reviewer: Scott Ahlgren) 11F11 (11F03 11F25)
  12. A note on special values of certain Dirichlet L-functions. Authors: B Ramakrishnan. Aust. Math. Soc. 83 (2011), no. 3, 435–438. (Reviewer: Giedrius Alkauskas) 11M06 (11D85 11E25 11F11 11M20)
  13. On the representation of integers as sums of two, three and four squares. Authors: B Ramakrishnan. Math. Student 79 (2010), no. 1-4, 117–141 (2011). 11D85
  14. Rankin's method and Jacobi forms of several variables. Authors: B Ramakrishnan and Brundaban Sahu. J. Aust. Math. Soc. 88 (2010), no. 1, 131–143. (Reviewer: Hidenori Katsurada) 11F50 (11F60)
  15. A canonical subspace of modular forms of half-integral weight. Authors: Sanoli Gun, M Manickam and B Ramakrishnan. Math. Ann. 347 (2010), no. 4, 899–916. (Reviewer: Shaun Cooper) 11F37 (11F11 11F27 11F32)
  16. On the representation of integers as sums of an odd number of squares. Authors: Sanoli Gun and B Ramakrishnan. Ramanujan J. 15 (2008), no. 3, 367–376. (Reviewer: Shaun Cooper) 11E25 (11D85 11F11)
  17. On special values of certain Dirichlet L-functions. Authors: Sanoli Gun and B Ramakrishnan. Ramanujan J. 15 (2008), no. 2, 275–280. (Reviewer: Valentin Blomer) 11E25 (11D85 11F11 11F20 11M06)
  18. On the lacunarity of two-eta-products. Authors: Shaun Cooper, Sanoli Gun and B Ramakrishnan. Georgian Math. J. 13 (2006), no. 4, 659–673. (Reviewer: Kaliyur R. Vasuki) 11F20 (11F11 11F25)
  19. On the Fourier expansions of Jacobi forms of half-integral weight. Authors: Brundaban Sahu and B Ramakrishnan. Int. J. Math. Math. Sci. 2006, Art. ID 14726, 11 pp. (Reviewer: Hidenori Katsurada) 11F30 (11F37 11F50)
  20. An Eichler-Zagier map for Jacobi forms of half-integral weight. Authors: M Manickam and B Ramakrishnan. Pacific J. Math. 227 (2006), no. 1, 143–150. (Reviewer: Yasushi Tokuno) 11F50 (11F37 11F46)
  21. Relations among Fourier coefficients of certain eta products. Authors: Shaun Cooper, Sanoli Gun, Michael Hirschhorn, B Ramakrishnan. Integers 5 (2005), no. 1, A16, 6 pp. (Reviewer: Matthew G. Boylan) 11F30
  22. Distribution of quadratic non-residues which are not primitive roots. Authors: Sanoli Gun, Brundaban Sahu, B Ramakrishnan, R Thangadurai. Math. Bohem. 130 (2005), no. 4, 387–396. (Reviewer: Wolfgang Schwarz) 11N69 (11A07 11A15)
  23. An estimate for a certain average of the special values of character twists of modular L-functions. Authors: M Manickam and B Ramakrishnan. Proc. Amer. Math. Soc. 133 (2005), no. 9, 2515–2517. (Reviewer: Matthew G. Boylan) 11F66 (11F11)
  24. An introduction to modular forms and Hecke operators. Elliptic curves, modular forms and cryptography. Authors: M Manickam and B Ramakrishnan. (Allahabad, 2000), 2223–245, Hindustan Book Agency, New Delhi, 2003. 11F11 (11F25 11F30)
  25. A note on certain divisibility properties of the Fourier coefficients of normalized Eisenstein series. Authors: B Ramakrishnan and R Thangadurai. Expo. Math. 21 (2003), no. 1, 75–82. (Reviewer: Kevin L. James) 11F30
  26. On Saito-Kurokawa correspondence of degree two for arbitrary level. Authors: M Manickam and B Ramakrishnan. J. Ramanujan Math. Soc. 17 (2002), no. 3, 149–160. (Reviewer: Aloys Krieg) 11F32 (11F11 11F46 11F50)
  27. Theory of newforms for the Maaß Spezialschar. Cohomology of arithmetic groups, L-functions and automorphic forms. Authors: B Ramakrishnan. Tata Inst. Fund. Res. Stud. Math., 15, Tata Inst. Fund. Res., Bombay, 2001. (Reviewer: T. C. Vasudevan) 11F37
  28. On the Eichler-Zagier map. Number theory and related topics. Authors: B Ramakrishnan. (Seoul, 1998), 29–52, Yonsei Univ. Inst. Math. Sci., Seoul, 2000. (Reviewer: M. Manickam) 11F50 (11F37 11F46)
  29. A brief introduction to modular forms. Cyclotomic fields and related topics. Authoes: B Ramakrishnan. (Pune, 1999), 219–238, Bhaskaracharya Pratishthana, Pune, 2000. (Reviewer: Imin Chen) 11F11 (11F03 11F25)
  30. On Shimura, Shintani and Eichler-Zagier correspondences. Authors: M Manickam and B Ramakrishnan. Trans. Amer. Math. Soc. 352 (2000), no. 6, 2601–2617. (Reviewer: Sukumar Das Adhikari) 11F32 (11F25 11F30 11F37 11F55 11F60)
  31. On exceptions of integral quadratic forms. Number theory. Authors: A K Lal and B Ramakrishnan. Number theory (Tiruchirapalli, 1996), 151–170, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998. (Reviewer: Rainer Schulze-Pillot) 11F30 (11E45 11F11 11F27)
  32. Modular forms which behave like theta series. Authors: Kalyan Chakraborty, B Ramakrishnan and A K Lal. Math. Comp. 66 (1997), no. 219, 1169–1183. (Reviewer: Michael C. Berg) 11F11 (11F27 11F30 11Y35)
  33. A note on Jacobi forms of higher degree. Authors: Kalyan Chakraborty, B Ramakrishnan and T C Vasudevan. Abh. Math. Sem. Univ. Hamburg 65 (1995), 89–93. (Reviewer: Rolf Berndt) 11F55 (11F46)
  34. A note on Hecke eigenforms. Authors: Kalyan Chakraborty and B Ramakrishnan. Arch. Math. (Basel) 63 (1994), no. 6, 509–516. (Reviewer: Pavel Guerzhoy) 11F30 (11F11 11F37 11F46)
  35. Theory of newforms. Authors: B Ramakrishnan. Bull. Allahabad Math. Soc. 8/9 (1993/94), 69–89 (1997). (Reviewer: Thomas R. Shemanske) 11F11 (11F25 11F37)
  36. On Saito-Kurokawa descent for congruence subgroups. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. Manuscripta Math. 81 (1993), no. 1-2, 161–182. (Reviewer: Aloys Krieg) 11F46 (11F37)
  37. Addendum: "On the theory of newforms of half-integral weight. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. [J. Number Theory 34 (1990), no. 2, 210–224; MR1042494]. J. Number Theory 42 (1992), no. 3, 369–371. (Reviewer: Solomon Friedberg) 11F37 (11F11)
  38. On a remark of Atkin-Lehner. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. J. Number Theory 40 (1992), no. 2, 251–253. (Reviewer: Angela Arenas) 11F25 (11F11)
  39. Diagonalising modular forms of half-integral weight. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. J. Number Theory 40 (1992), no. 1, 32–37. (Reviewer: Jannis A. Antoniadis) 11F37
  40. On the theory of newforms of half-integral weight. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. J. Number Theory 34 (1990), no. 2, 210–224. (Reviewer: Solomon Friedberg) 11F37 (11F11)
  41. On Shintani correspondence. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. Proc. Indian Acad. Sci. Math. Sci. 99 (1989), no. 3, 235–247. (Reviewer: Hiroshi Saito) 11F11 (11F30)
  42. Hecke operators on modular forms of half-integral weight. Authors: M Manickam, B Ramakrishnan and T C Vasudevan. Arch. Math. (Basel) 51 (1988), no. 4, 343–352. (Reviewer: Thomas R. Shemanske) 11F37 (11F11)