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  • RANKIN’S METHOD AND JACOBI FORMS OF SEVERAL VARIABLES

  • Part of
  • B. RAMAKRISHNAN, BRUNDABAN SAHU
  • Journal:
    Journal of the Australian Mathematical Society / Volume 88 / Issue 1 / February 2010
    Published online by Cambridge University Press:
    26 January 2010, pp. 131-143
    Print publication:
    February 2010
    • Article
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  • Following R. A. Rankin’s method, D. Zagier computed the nth Rankin–Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2, computed the inner product of this Rankin–Cohen bracket with a cusp form f of weight k=k1+k2+2n and showed that this inner product gives, up to a constant, the special value of the Rankin–Selberg convolution of f and g. This result was generalized to Jacobi forms of degree 1 by Y. Choie and W. Kohnen. In this paper, we generalize this result to Jacobi forms defined over ℋ×ℂ(g,1).