A Sato–Tate law for GL (3)

  • Valentin Blomer

    Georg-August-Universität Göttingen, Germany
  • Jack Buttcane

    Georg-August-Universität Göttingen, Germany
  • Nicole Raulf

    Université des Sciences et Technologies de Lille, Villeneuve d'Ascq, France


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