THE SUP-NORM PROBLEM FOR AUTOMORPHIC CUSP FORMS OF PGL(n,Z[i])

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（2023）

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摘要

Let phi be an L-2-normalized Hecke-Maa beta cusp form on the locally symmetric space X := PGL(n)(Z[i])\PGL(n)(C)/PUn. If omega is a compact subset of X, then we prove the bound ||phi|Omega||(infinity) < 0 depending only on n, where lambda(phi) is the Laplace eigenvalue of phi.

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关键词

Automorphic forms in higher rank,sup-norm problem,Hecke operators,trace formula,diophantine approximation,amplification

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