Document Type
Article
Version
Final Published Version
Publication Title
Annales Scientifiques de l’École Normale Supérieure
Volume
57
Publication Date
2024
Abstract
Let F be a number field and n > 1 an integer. The universal family is the set F of all unitary cuspidal automorphic representations on GLn over F, ordered by their analytic conductor. We prove an asymptotic for the size of the truncated universal family F(Q) as Q ! 1, under a spherical assumption at the archimedean places when n > 3. We interpret the leading term constant geometrically and conjecturally determine the underlying Sato–Tate measure. Our methods naturally provide uniform Weyl laws with logarithmic savings in the level and strong quantitative bounds on the non-tempered discrete spectrum for GLn.
Publisher's Statement
First published in Annales Scientifiques de l’École Normale Supérieure in Volume 57 (2024), by the Société Mathématique de France
Citation
Brumley, Farrell, and Djordje Milićević. 2024. “Counting Cusp Forms by Analytic Conductor.” Annales Scientifiques de l’École Normale Supérieure 57 (5): 1473–1597. https://doi.org/10.24033/asens.2595.
DOI
10.24033/asens.2595
