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arXiv · 1505.07285

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

Jasmin Matz·Nicolas Templier
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Abstract

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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Jasmin Matz, Nicolas Templier. 2015-05-27. Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n). https://doi.org/10.2140/ant.2021.15.1343

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