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Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n)

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arxiv 1505.07285 v8 pith:57PB3GS3 submitted 2015-05-27 math.NT math.RT

Jasmin Matz , Nicolas Templier This is my paper · ORCID
classification math.NTmath.RT
keywords familiesaveragededuceequidistributionformssato-tatesquarecusp
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We establish the Sato-Tate equidistribution of Hecke eigenvalues on average for families of Hecke--Maass cusp forms on SL(n,R)/SO(n). For each of the principal, symmetric square and exterior square L-functions we verify that the families are essentially cuspidal and deduce the level distribution with restricted support of the low-lying zeros. We also deduce average estimates toward Ramanujan.

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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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