Abstract
Let F be a Siegel cusp form of weight k and genus n > 1 with Fourier-Jacobi coefficients f m . In this article, we estimate the growth of the Petersson norms of f m , where m runs over an arithmetic progression. This result sharpens a recent result of Kohnen [5].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Böcherer S., Bruinier J. H., Kohnen W.: Non-vanishing of scalar products of Fourier-Jacobi coefficients of Siegel cusp forms. Math. Ann. 313, 1–13 (1999)
Kohnen W., Skoruppa N.-P.: A certain Dirichlet series attached to Siegel modular forms of degree two. Invent. Math. 95, 541–558 (1989)
Kohnen W.: On characteristic twists of certain Dirichlet series. Mem. Fac. Sci. Kyushu Univ. Ser. A 47, 103–117 (1993)
Kohnen W., Krieg A., Sengupta J.: Characteristic twists of a Dirichlet series for Siegel cusp forms. Manuscripta Math. 87, 489–499 (1995)
Kohnen W.: On the growth of the Petersson norms of Fourier-Jacobi coefficients of Siegel cusp forms. Bull. Lond. Math. Soc. 43, 717–720 (2011)
Krieg A.: A Dirichlet series for modular forms of degree n. Acta Arith. 59, 243–259 (1991)
de A. Pribitkin W.: On the sign changes of coefficients of general Dirichlet series. Proc. Amer. Math. Soc. 136, 3089–3094 (2008)
de A. Pribitkin W.: On the oscillatory behavior of certain arithmetic functions associated with automorphic forms. J. Number Theory 131, 2047–2060 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gun, S., Kumar, N. A note on Fourier-Jacobi coefficients of Siegel modular forms. Arch. Math. 101, 519–524 (2013). https://doi.org/10.1007/s00013-013-0586-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-013-0586-0