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arXiv · 1710.00362

On sup-norm bounds part I: ramified Maa{\ss} newforms over number fields

Edgar Assing
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Abstract

We prove new upper bounds for the sup-norm of Hecke Maa{\ss} newforms on $GL(2)$ over a number field. Our newforms are more general than those considered in a recent paper by Blomer, Harcos, Maga, and Mili\`cevi\`c: we do not require square free level. Furthermore, we allow for non-trivial central character. Over the rationals we cover the best bounds as obtained by Saha.

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Edgar Assing. 2017-10-01. On sup-norm bounds part I: ramified Maa{\ss} newforms over number fields. https://arxiv.org/abs/1710.00362

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