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초록

In this paper, we investigate a Zagier duality between the Fourier coefficients of harmonic Maass–Jacobi–Poincaré series and those of weakly skew-holomorphic Jacobi–Poincaré series. We also verify a similar duality involving the skew-holomorphic Jacobi–Eisenstein series. As an application of these duality results, we show that the weakly skew-holomorphic Poincaré series and the skew-holomorphic Jacobi–Eisenstein series are orthogonal to the space of skew-holomorphic Jacobi cusp forms. Moreover, in the case of integral weight and level one, we obtain the rationality for the coefficients of the skew-holomorphic Jacobi–Eisenstein series. Combined with the duality result for the Jacobi–Eisenstein series, this implies the rationality of the constant term in the holomorphic part of the harmonic Maass–Jacobi–Poincaré series.

키워드