JournalscmhVol. 89, No. 4pp. 895–919

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
A Sato–Tate law for GL (3) cover


We consider statistical properties of Hecke eigenvalues Aj(p,1)A_j(p, 1) for fixed pp as ϕj\phi_j runs through a basis of Hecke–Maaß cusp forms for the group SL3(Z)\mathrm{SL}_3(\mathbb{Z}). We show that almost all of them satisfy the Ramanujan conjecture at pp 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