English

Lower bounds for Maass forms on semisimple groups

Number Theory 2020-04-22 v4 Analysis of PDEs

Abstract

Let GG be an anisotropic semisimple group over a totally real number field FF. Suppose that GG is compact at all but one infinite place v0v_0. In addition, suppose that Gv0G_{v_0} is R\mathbb{R}-almost simple, not split, and has a Cartan involution defined over FF. If YY is a congruence arithmetic manifold of non-positive curvature associated to GG, we prove that there exists a sequence of Laplace eigenfunctions on YY whose sup norms grow like a power of the eigenvalue.

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Cite

@article{arxiv.1604.02019,
  title  = {Lower bounds for Maass forms on semisimple groups},
  author = {Farrell Brumley and Simon Marshall},
  journal= {arXiv preprint arXiv:1604.02019},
  year   = {2020}
}
R2 v1 2026-06-22T13:27:28.083Z