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Sup norm on $\text{PGL}_n$ in depth aspect

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arxiv 1809.00617 v1 pith:W33VVFZD submitted 2018-09-03 math.NT

classification math.NT
keywords automorphicnormrepresentationtextaspectassociatedbelongingbound
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abstract

In this short paper we give the sub-local upper bound for the sup norm of an automorphic form on $\text{PGL}_n$, whose associated automorphic representation has finite conductor $C(\pi)=p^c$ with $c\rightarrow \infty$, and its local component at the place of ramification is a minimal vector belonging to an irreducible representation with generic induction datum.

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  1. Squarefree numbers in short intervals: explicit and formalized

    math.NT 2026-08 conditional novelty 6.0 of 10

    For intervals of length H = X^{1/5 - 2/90935 + ε}, the number of squarefree integers differs from (6/π²)H by at most an explicit constant times H X^{-ε/10^{25}}.

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