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Pré-Publication, Document De Travail Année : 2022

Counting cusp forms by analytic conductor

Djordje Milićević
  • Fonction : Auteur

Résumé

The universal family is the set of cuspidal automorphic representations of bounded analytic conductor on ${\rm GL}_n$ over a number field. We prove an asymptotic for the universal family, under a spherical assumption at the archimedean places when $n\geqslant 3$. We interpret the leading term constant geometrically and conjecturally determine the underlying Sato--Tate measure. Our methods naturally provide uniform Weyl laws with explicit level savings and strong quantitative bounds on the non-tempered discrete spectrum for ${\rm GL}_n$.

Dates et versions

hal-03913420 , version 1 (26-12-2022)

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Farrell Brumley, Djordje Milićević. Counting cusp forms by analytic conductor. 2022. ⟨hal-03913420⟩
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