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\(L^4\)-norms of Hecke newforms of large level

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Abstract

We prove a new upper bound for the \(L^4\)-norm of a holomorphic Hecke newform of large fixed weight and prime level \(q\rightarrow \infty \). This is achieved by proving a sharp mean value estimate for a related \(L\)-function on \(GL(6)\).

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Notes

  1. These authors actually proved their results for Hecke-Maass forms, but very similar arguments would work for holomorphic Hecke newforms as well.

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Acknowledgments

While working on this paper, the authors were supported by a Grant from the European Research Council (Grant agreement number 258713).

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  1. Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstrasse 3-5, 37073, Göttingen, Germany

    Jack Buttcane & Rizwanur Khan

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  1. Jack Buttcane
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  2. Rizwanur Khan
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Correspondence to Rizwanur Khan.

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Buttcane, J., Khan, R. \(L^4\)-norms of Hecke newforms of large level. Math. Ann. 362, 699–715 (2015). https://doi.org/10.1007/s00208-014-1142-3

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  • DOI: https://doi.org/10.1007/s00208-014-1142-3

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