Abstract
We characterize Siegel cusp forms in the space of Siegel modular forms of small weight \(k \ge n+4\) on the congruence subgroups \(\Gamma ^n_0(N)\) of any degree n and any level N, by a suitable growth of their Fourier coefficients (e.g., by the well known Hecke bound) at any one of the cusps. For this, we use the formalism of Jacobi forms and the ‘Witt-operator’ on modular forms.
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Acknowledgments
We thank the Department of Mathematics, University of Tokyo, Indian Institute of Science, Bangalore and HRI, Allahabad, where parts of this work was done, for providing a very pleasant working atmosphere. Finally, the second author acknowledges financial support from UGC Center for Advanced Studies, DST India and IISc., Bangalore during this work.
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Böcherer, S., Das, S. Cuspidality and the growth of Fourier coefficients: small weights. Math. Z. 283, 539–553 (2016). https://doi.org/10.1007/s00209-015-1609-2
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DOI: https://doi.org/10.1007/s00209-015-1609-2