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Saito-Kurokawa liftings of level \(N\) and practical construction of Jacobi forms. (English) Zbl 1284.11085
In the paper under review the author derives a generalization of the Saito-Kurokawa lift to the case of Jacobi forms of arbitrary level including characters. The lift is described explicitly on the basis of the Fourier expansions. The paper describes the Hecke theory, including operators at bad primes. The final section contains explicit descriptions of Jacobi forms of level \(N\leq 5\).

MSC:
11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F50 Jacobi forms
11F30 Fourier coefficients of automorphic forms
11F37 Forms of half-integer weight; nonholomorphic modular forms
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