Distinguishing finite group characters and refined local-global phenomena

Kimball Martin ¹   ; Nahid Walji ²

¹ Department of Mathematics University of Oklahoma Norman, OK 73019, U.S.A.
² The American University of Paris 75007 Paris, France

Acta Arithmetica, Tome 179 (2017) no. 3, pp. 277-300

Résumé

Serre obtained a sharp bound on how often two irreducible degree $n$ complex characters of a finite group can agree, which tells us how many local factors determine an Artin $L$-function. We consider the more delicate question of finding a sharp bound when these objects are primitive, and answer this question for $n=2,3$. This provides some insight on refined strong multiplicity one phenomena for automorphic representations of $\operatorname{GL}(n)$. For general $n$, we also answer the character question for the families $\operatorname{PSL}(2,q)$ and $\operatorname{SL}(2,q)$.

Détail

DOI : 10.4064/aa170120-1-5

Keywords: serre obtained sharp bound often irreducible degree complex characters finite group agree which tells many local factors determine artin l function consider delicate question finding sharp bound these objects primitive answer question provides insight refined strong multiplicity phenomena automorphic representations operatorname general answer character question families operatorname psl operatorname