Abstract
Let \(f\) be a Hecke–Maass cuspidal newform of square-free level \(N\) and Laplacian eigenvalue \(\lambda \). It is shown that \(\left||f \right||_\infty \ll _{\lambda ,\epsilon } N^{-\frac{1}{6}+\epsilon } \left||f \right||_2\) for any \(\epsilon >0\).
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We thank the referee for his/her helpful comments.
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G. Harcos was partially supported by EC and OTKA grants ERG 239277, K 72731, PD 75126; N. Templier was partially supported by Grant #209849 from the Simons Foundation.
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Harcos, G., Templier, N. On the sup-norm of Maass cusp forms of large level. III. Math. Ann. 356, 209–216 (2013). https://doi.org/10.1007/s00208-012-0844-7
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DOI: https://doi.org/10.1007/s00208-012-0844-7