An explicit conductor formula for ${\mathrm{GL}}_n\times {\mathrm{GL}}_1$

Abstract

We prove an explicit formula for the conductor of an irreducible, admissible representation of ${\mathrm{GL}}_n(F)$ twisted by a character of $F^{\times }$ where the field $F$ is local and non-archimedean. As a consequence, we quantify the number of character twists of such a representation of fixed conductor.

References in corpus (2)

• On the order of vanishing of newforms at cusps
• Large values of newforms on GL(2) with highly ramified central character