Bruce C. Berndt

Articles in Scholarly Journals [Incomplete List]

  1. Partition identities and Ramanujan's modular equations
    Journal of Combinatorial Theory, Series A, vol. 114, no. 6, pp. 1024–1045, 2007
  2. A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook
    The Ramanujan Journal, vol. 13, no. 1-3, pp. 27–37, 2007
  3. Proceedings of the American Mathematical Society, vol. 135, no. 01, pp. 129–135, 2007
  4. Weighted Divisor Sums and Bessel Function Series
    Mathematische Annalen, vol. 335, no. 2, pp. 249–283, 2006
  5. International Journal of Number Theory, vol. 2, no. 1, p. 111, 2006
  6. A continued fraction from Ramanujan’s lost notebook
    Aequationes mathematicae, vol. 69, no. 3, pp. 257–262, 2005
  7. Cranks and dissections in Ramanujan's lost notebook
    Journal of Combinatorial Theory, Series A, vol. 109, no. 1, pp. 91–120, 2005
  8. Continued fractions with three limit points
    Advances in Mathematics, vol. 192, no. 2, pp. 231–258, 2005
  9. Transactions of the American Mathematical Society, vol. 357, no. 11, pp. 4379–4413, 2005
  10. International Journal of Number Theory, vol. 1, no. 3, p. 333, 2005
  11. New theorems on the parity of partition functions
    Journal f�r die reine und angewandte Mathematik (Crelles Journal), vol. 2004, no. 566, pp. 91–109, 2004
  12. Proceedings of the American Mathematical Society, vol. 132, no. 10, pp. 2983–2989, 2004
  13. A New Identity for (q;q) 10 with an Application to Ramanujan's Partition Congruence Modulo 11
    The Quarterly Journal of Mathematics, vol. 55, no. 1, pp. 13–30, 2004
  14. Finite trigonometric sums and class numbers
    Mathematische Annalen, vol. 330, no. 3, pp. 551–575, 2004
  15. Combinatorial Proofs of Identities in Ramanujan?s Lost Notebook Associated with the Rogers-Fine Identity and False Theta Functions
    Annals of Combinatorics, vol. 7, no. 4, pp. 409–423, 2003
  16. Transactions of the American Mathematical Society, vol. 355, no. 06, pp. 2397–2412, 2003
  17. A PAGE ON EISENSTEIN SERIES IN RAMANUJANS LOST NOTEBOOK
    Glasgow Mathematical Journal, vol. 45, no. 1, pp. 123–129, 2003
  18. Theorems on partitions from a page in Ramanujan's lost notebook
    Journal of Computational and Applied Mathematics, vol. 160, no. 1-2, pp. 53–68, 2003
  19. International Journal of Mathematics, vol. 14, no. 4, p. 437, 2003
  20. A quasi-theta product in Ramanujans lost notebook
    Mathematical Proceedings of the Cambridge Philosophical Society, vol. 135, no. 1, pp. 11–18, 2003
  21. The Ramanujan Journal, vol. 7, no. 1/3, pp. 9–38, 2003
  22. The Ramanujan Journal, vol. 7, no. 1/3, pp. 321–331, 2003
  23. Explicit evaluations and reciprocity theorems for finite trigonometric sums
    Advances in Applied Mathematics, vol. 29, no. 3, pp. 358–385, 2002
  24. Asymptotic Formulas for Two Continued Fractions in Ramanujan's Lost Notebook
    Journal of the London Mathematical Society, vol. 65, no. 2, pp. 271–284, 2002
  25. International Mathematics Research Notices, vol. 2002, no. 21, p. 1077, 2002
  26. International Mathematics Research Notices, vol. 2002, no. 32, p. 1723, 2002
  27. An integral of Dedekind An integral of Dedekind An integral of Dedekind An integral of Dedekind eta-functions in Ramanujans lost notebook
    Journal f�r die reine und angewandte Mathematik (Crelles Journal), vol. 2002, no. 551, pp. 33–39, 2002
  28. A multi-variable theta product
    Indagationes Mathematicae, vol. 13, no. 1, pp. 11–22, 2002
  29. On Ramanujan's Quartic Theory of Elliptic Functions
    Journal of Number Theory, vol. 88, no. 1, pp. 129–156, 2001
  30. The Books Studied by Ramanujan in India
    The American Mathematical Monthly, vol. 107, no. 7, p. 595, 2000
  31. Transactions of the American Mathematical Society, vol. 352, no. 05, pp. 2157–2178, 2000
  32. The Ramanujan Journal, vol. 4, no. 1, pp. 81–114, 2000
  33. The Ramanujan Journal, vol. 4, no. 1, pp. 41–42, 2000
  34. The Rogers–Ramanujan continued fraction
    Journal of Computational and Applied Mathematics, vol. 105, no. 1-2, pp. 9–24, 1999
  35. Transactions of the American Mathematical Society, vol. 349, no. 06, pp. 2125–2174, 1997
  36. The Ramanujan Journal, vol. 1, no. 1, pp. 53–74, 1997
  37. Ramanujan's Association with Radicals in India
    The American Mathematical Monthly, vol. 104, no. 10, p. 905, 1997
  38. Ramanujan's Theories of Elliptic Functions to Alternative Bases
    Transactions of the American Mathematical Society, vol. 347, no. 11, p. 4163, 1995
  39. A New Class of Theta-Function Identities Originating in Ramanujan′s Notebooks
    Journal of Number Theory, vol. 48, no. 2, pp. 224–242, 1994
  40. Ramanujan--For Lowbrows
    The American Mathematical Monthly, vol. 100, no. 7, p. 644, 1993
  41. Ramanujan's identities for eta-functions
    Mathematische Annalen, vol. 292, no. 1, pp. 561–573, 1992
  42. Ramanujan's inversion formulas for the lemniscate and allied functions
    Journal of Mathematical Analysis and Applications, vol. 160, no. 2, pp. 504–524, 1991
  43. Some elegant approximations and asymptotic formulas of Ramanujan
    Journal of Computational and Applied Mathematics, vol. 37, no. 1-3, pp. 35–41, 1991
  44. Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
    The American Mathematical Monthly, vol. 95, no. 7, p. 585, 1988
  45. The Gamma Function and the Hurwitz Zeta-Function
    The American Mathematical Monthly, vol. 92, no. 2, p. 126, 1985
  46. Ramanujan's Quarterly Reports
    Bulletin of the London Mathematical Society, vol. 16, no. 5, pp. 449–489, 1984
  47. SIAM Journal on Mathematical Analysis, vol. 15, no. 1, Article ID 0515011, 1984
  48. Chapter 11 of Ramanujan's Second Notebook
    Bulletin of the London Mathematical Society, vol. 15, no. 4, pp. 273–320, 1983
  49. The Quarterly Reports of S. Ramanujan
    The American Mathematical Monthly, vol. 90, no. 8, p. 505, 1983
  50. Half Gauss sums
    Mathematische Annalen, vol. 249, no. 2, pp. 115–125, 1980
  51. Sums of gauss, jacobi, and jacobsthal1
    Journal of Number Theory, vol. 11, no. 3, pp. 349–398, 1979
  52. A new class of Bessel function integrals
    Aequationes Mathematicae, vol. 16, no. 1-2, pp. 183–186, 1977
  53. Dedekind sums and class numbers
    Monatshefte f�r Mathematik, vol. 84, no. 4, pp. 265–273, 1977
  54. Character analogues of the poisson and Euler-MacLaurin summation formulas with applications
    Journal of Number Theory, vol. 7, no. 4, pp. 413–445, 1975
  55. A Generalization of a Theorem of Gauss on Sums Involving [ x ]
    The American Mathematical Monthly, vol. 82, no. 1, p. 44, 1975
  56. SIAM Journal on Mathematical Analysis, vol. 6, no. 6, Article ID 0506085, 1975
  57. Identities Involving the Coefficients of a Class of Dirichlet Series. VII
    Transactions of the American Mathematical Society, vol. 201, p. 247, 1975
  58. SIAM Review, vol. 16, no. 4, Article ID 1016097, 1974
  59. Generalized Dedekind Eta-Functions and Generalized Dedekind Sums
    Transactions of the American Mathematical Society, vol. 178, p. 495, 1973
  60. A New Proof of the Functional Equation of Dirichlet L-Functions
    Proceedings of the American Mathematical Society, vol. 37, no. 2, p. 355, 1973
  61. Two New Proofs of Lerch's Functional Equation
    Proceedings of the American Mathematical Society, vol. 32, no. 2, p. 403, 1972
  62. The Functional Equation of Some Dirichlet Series. II
    Proceedings of the American Mathematical Society, vol. 31, no. 1, p. 24, 1972
  63. The Functional Equation of Some Dirichlet Series
    Proceedings of the American Mathematical Society, vol. 29, no. 3, p. 457, 1971
  64. The number of zeros of the Dedekind zeta-function on the critical line
    Journal of Number Theory, vol. 3, no. 1, pp. 1–6, 1971
  65. On the average order of a class of arithmetical functions, I
    Journal of Number Theory, vol. 3, no. 2, pp. 184–203, 1971
  66. On the average order of a class of arithmetical functions, II*1
    Journal of Number Theory, vol. 3, no. 3, pp. 288–305, 1971
  67. Erratum: On the Zeros of the Riemann Zeta-Function
    Proceedings of the American Mathematical Society, vol. 24, no. 4, p. 839, 1970
  68. Identities Involving the Coefficients of a Class of Dirichlet Series.
    Transactions of the American Mathematical Society, vol. 149, no. 1, p. 179, 1970
  69. On the Zeros of the Riemann Zeta-Function
    Proceedings of the American Mathematical Society, vol. 22, no. 1, p. 183, 1969
  70. Identities Involving the Coefficients of a Class of Dirichlet Series. III
    Transactions of the American Mathematical Society, vol. 146, p. 323, 1969