Abstract:
This paper deals with Jacobi forms Φ on ?×ℂ. The Rankin–Selberg doubling method is employed to study properties of the standard L-function of Hecke–Jacobi eigenforms. It is shown that every analytic Klingen–Jacobi Eisenstein series attached to Φ has a meromorphic continuation on the whole complex plane. Hecke–Jacobi cusp eigenforms of weight k > 4 and k≡ 0 mod 4 can written explicitly as a linear combination of theta series. Finally the basis problem of Jacobi forms of square-free index is solved.
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Received: 12 March 2000 / Revised version: 17 September 2001
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Heim, B. L-functions for Jacobi forms and the basis problem. manuscripta math. 106, 489–503 (2001). https://doi.org/10.1007/s229-001-8029-8
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DOI: https://doi.org/10.1007/s229-001-8029-8