Abstract
We prove the meromorphic continuation and the functional equation of a twisted real-analytic Hermitain Eisenstein series of Klingen type, and as a consequence, deduce similar properties for the twisted Dirichlet series associated to a pair of Hermitian modular forms involving their Fourier–Jacobi coefficients. As an application of our result, we prove that infinitely many of the Fourier–Jacobi coefficients of a non-zero Hermitian cusp form do not vanish in any non-trivial arithmetic progression.
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Acknowledgements
S. Das thanks IISc. Bangalore, DST (India) and UGC centre for advanced studies for financial support. During the preparation of this work S. Das was supported by a MATRICS Grant MTR/2017/000496 from DST-SERB, India. The second author thanks Science and Engineering Research Board (SERB), India for financial support through national postdoctoral fellowship - NPDF (PDF/2016/001598).
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Communicated by Jens Funke.
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Das, S., Jha, A.K. Analytic properties of twisted real-analytic Hermitian Klingen type Eisenstein series and applications . Abh. Math. Semin. Univ. Hambg. 89, 105–116 (2019). https://doi.org/10.1007/s12188-019-00206-7
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DOI: https://doi.org/10.1007/s12188-019-00206-7