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arXiv · 2111.01893

The sup-norm problem beyond the newform

Edgar Assing
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Abstract

In this note we take up the classical sup-norm problem for automorphic forms and view it from a new angle. Given a twist minimal automorphic representation $\pi$ we consider a special small $GL_2(\mathbb{Z}_p)$-type $V$ in $\pi$ and proof global sup-norm bounds for an average over an orthonormal basis of $V$. We achieve a non-trivial saving when the dimension of $V$ grows.

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Edgar Assing. 2021-11-02. The sup-norm problem beyond the newform. https://doi.org/10.1017/s0305004124000021

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