Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL₂

2011/03/12 by Simon Marshall, Marshall, Simon
Mathematics · #11F41 #11F75 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F41 #msc:11F75

paper · pdf · doi:10.48550/arxiv.1103.2472

19 pages

arxiv created 2011/03/12 · arxiv updated 2011/03/15

Abstract

We prove an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL₂ over any number field which is not totally real. Our proof involves the theory of p-adically completed cohomology developed by Calegari and Emerton, and a bound for the growth of coinvariants in certain finitely generated non-commutative Iwasawa modules.

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