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Recent results by Abert, Bergeron, Biringer et al., Finis, Lapid and Mueller,and Shin and Templier have extended the limit multiplicity property to quitegeneral classes of groups and sequences of level subgroups. Automorphicrepresentations in the limit multiplicity problem are traditionally countedwith multiplicity according to the number of fixed vectors of a level subgroup;our goal is to perform a slightly more refined analysis and count onlyautomorphic representations with a given conductor with multiplicity 1.

Refined limit multiplicity for varying conductor