L-functions attached to Jacobi forms of degree n. II: Functional equation (Q2640640)
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| English | L-functions attached to Jacobi forms of degree n. II: Functional equation |
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L-functions attached to Jacobi forms of degree n. II: Functional equation (English)
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1991
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The paper is a continuation of part I [J. Reine Angew. Math. 401, 122-156 (1989; Zbl 0671.10023)]. In this second part, the standard zeta function D(s,f) for a Jacobi cusp form f of degree n is defined after Shintani and its analytic continuation and functional equation are proved. In the previous paper, a certain Rankin-Selberg convolution Z(s,f) was introduced and its Euler product decomposition (``the basic identity'') was proved. The present paper is mainly devoted to the explicit calculation of each local factor of Z(s,f). This yields a simple relation between D(s,f) and Z(s,f). Then the analytic continuation and functional equation of D(s,f) are direct consequences of those of Z(s,f) proved in the previous paper.
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zeta function
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Hecke theory
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Hecke operators
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Jacobi cusp form
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analytic continuation
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functional equation
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