On Murmurations and Trace Formulas

Abstract

In recent work with Bober, Booker, Lee, Seymour-Howell, and Zubrilina, we proved murmuration behavior for Maass forms in the eigenvalue aspect and for modular forms in the weight aspect. Both used an approach based on the Selberg trace formula. But different trace formulas, including those due to Kuznetsov or Petersson, offer different variations. We examine murmurations from the perspective of different trace formulas and outline several families of $L$-functions where one can likely prove additional murmuration behavior.