On the Ramanujan conjecture over number fields

2011/06/22 by Valentin Blomer, Farrell Brumley · 6 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Finite Group Theory Research

paper · pdf · doi:10.4007/annals.2011.174.1.18

Abstract

We extend to an arbitrary number field the best known bounds towards Ramanujan for the group GLn, n = 2, 3, 4. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units.

Citations

• On Euler Products and the Classification of Automorphic Representations I
• On Certain L-Functions

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• The second moment of GL(2)× GL(2) Rankin-Selberg L-functions in the level aspect
• Large sieves for GL_n and applications
• The Ramanujan conjecture and its applications. [europepmc]

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