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\(L^4\)-norms of the holomorphic dihedral forms of large level

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Abstract

Let \(\widetilde{f}\) be an \(L^2\)-normalized holomorphic dihedral form of prime level \(q\) and fixed weight. We show that, for any \(\varepsilon >0,\)

$$\begin{aligned} \Vert \widetilde{f} \Vert _4^4 \ll _{\varepsilon }q^{-\frac{11}{12}-\frac{1}{3}\delta + \varepsilon }, \end{aligned}$$

for some \(\delta >0\).

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Authors and Affiliations

  1. Department of Mathematics, Washington State University, Pullman, WA, 99164-3113, USA

    Sheng-Chi Liu

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  1. Sheng-Chi Liu
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Correspondence to Sheng-Chi Liu.

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Communicated by Jens Funke.

The author was supported by AMS-Simons Travel Grant.

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Liu, SC. \(L^4\)-norms of the holomorphic dihedral forms of large level. Abh. Math. Semin. Univ. Hambg. 85, 53–57 (2015). https://doi.org/10.1007/s12188-014-0100-z

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  • DOI: https://doi.org/10.1007/s12188-014-0100-z

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