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arXiv · 2305.15162

Norm bounds on Eisenstein series

Dubi Kelmer·Alex Kontorovich·Christopher Lutsko
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Abstract

We study the sup-norm and mean-square-norm problems for Eisenstein series on certain arithmetic hyperbolic orbifolds, producing sharp exponents for the modular surface and Picard 3-fold. The methods involve bounds for Epstein zeta functions, and counting restricted values of indefinite quadratic forms at integer points.

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Dubi Kelmer, Alex Kontorovich, Christopher Lutsko. 2023-05-24. Norm bounds on Eisenstein series. https://arxiv.org/abs/2305.15162

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