Rankin's method and Jacobi forms of several variables

2008/08/18 by Ramakrishnan, B., Sahu, Brundaban
#11F50 #11F60 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0808.2395

Abstract

Following Rankin's method, D. Zagier computed the n-th Rankin-Cohen bracket of a modular form g of weight k₁ with the Eisenstein series of weight k₂ and then 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, upto 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 \mathcal H × \mathbb C^{(g, 1)}.

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