On the Ramanujan conjecture over number fields

2010/03/02 by Valentin Blomer, Farrell Brumley, Blomer, Valentin +1 · 9 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Combinatorics #Conjecture #Field (mathematics) #Finite Group Theory Research #Group (periodic table) #Mathematics #Physics #Pure mathematics #Ramanujan's sum #math.NT #math.RT #msc:11F70

paper · pdf · doi:10.4007/annals.2011.174.1.18

published in Annals of Mathematics 174(1), 581-605 (Princeton University) · Minor corrections from previous version. To appear in Annals of Mathematics

arxiv created 2011/03/15 · arxiv updated 2011/03/16 · openalex publication_date 2011/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Cited by

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• Triality and adjoint lifting for GL(3)
• Stationary phase analysis for analytic newvectors and application to subconvexity problems
• The second moment of GL(2)× GL(2) Rankin-Selberg L-functions in the level aspect
• Large sieves for GL_n and applications
• Soft bounds for local triple products and the subconvexity-QUE implication for GL₂
• On the spectral aspect density hypothesis and application
• Ramanujan–Petersson conjecture [wikipedia]
• The Ramanujan conjecture and its applications. [europepmc]

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