Harmonic Analysis and Hecke Operators

  • Hee Oh
Chapter

Abstract

We first construct new uniform pointwise bounds for the matrix coefficients of infinite dimensional unitary representations of a reductive algebraic group defined over a local field k with semisimple k-rank at least 2, [22]. We explain how this information on local harmonic analysis yields norm estimates for (global) Hecke operators on L 2(Γ\G) for a connected almost simple simply connected ℚ-group G and its congruence subgroups Γ, [6]. With the tool of Hecke operators, we settle a question of Linnik raised in the early sixties on the distribution of integer points of Diophantine type varieties when the varieties are homogeneous spaces of a reductive algebraic group over ℚ, [11]. Lastly we discuss how to obtain evenly distributed sequences on the spheres S n (n ≥ 4) [23], generalizing the work of Lubotzky, Phillips and Sarnak on S 2 and S 3 ([19], [20]).

Keywords

Unitary Representation Automorphic Form Integer Point Congruence Subgroup Orthogonal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Hee Oh
    • 1
  1. 1.Mathematics departmentPrinceton UniversityPrincetonUSA

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