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RANKIN’S METHOD AND JACOBI FORMS OF SEVERAL VARIABLES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  26 January 2010

B. RAMAKRISHNAN  and
BRUNDABAN SAHU
B. RAMAKRISHNAN
Affiliation:
Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India (email: ramki@hri.res.in)
BRUNDABAN SAHU*
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland (email: brundaban.sahu@ucd.ie)
*
✉For correspondence; e-mail: brundaban.sahu@ucd.ie
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Abstract

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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).

Keywords

Rankin’s methodJacobi forms of higher degreeRankin–Cohen differential operators

MSC classification

Secondary: 11F50: Jacobi forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 1 , February 2010 , pp. 131 - 143
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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