On the balanced Voronoï formula for GL$_N$

Abstract

Miller and F. Zhou have proved a balanced Voronoï summation formula for GL$_N$ over $\mathbb{Q}$, which allows one to control the dimensions of the Kloosterman sums appearing on either side of the Voronoï formula. In this note, we prove a balanced Voronoï formula over an arbitrary number field, starting with the Voronoï summation formula of A. Ichino and N. Templier over number fields, allowing one to extend recent results on spectral reciprocity laws to number fields, in special cases.