A Sato–Tate law for GL (3)
Valentin Blomer
Georg-August-Universität Göttingen, GermanyJack Buttcane
Georg-August-Universität Göttingen, GermanyNicole Raulf
Université des Sciences et Technologies de Lille, Villeneuve d'Ascq, France
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Abstract
We consider statistical properties of Hecke eigenvalues for fixed as runs through a basis of Hecke–Maaß cusp forms for the group . We show that almost all of them satisfy the Ramanujan conjecture at and that their distribution is governed by the Sato–Tate law.
Cite this article
Valentin Blomer, Jack Buttcane, Nicole Raulf, A Sato–Tate law for GL (3). Comment. Math. Helv. 89 (2014), no. 4, pp. 895–919
DOI 10.4171/CMH/337