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L-functions attached to Jacobi forms of degree n. II: Functional equation. (English) Zbl 0721.11022
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.
Reviewer: A.Murase (Kyoto)

MSC:
11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F50 Jacobi forms
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References:
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