Local Maaß forms and Eichler–Selberg relations for negative-weight vector-valued mock modular forms

Joshua Males and Andreas Mono

Vol. 322 (2023), No. 2, 381–406

DOI: 10.2140/pjm.2023.322.381

Abstract

By comparing two different evaluations of a modified (à la Borcherds) higher Siegel theta lift on even lattices of signature $(r,s)$, we prove Eichler–Selberg relations for a wide class of negative-weight vector-valued mock modular forms. In doing so, we detail several properties of the lift, as well as showing that it produces an infinite family of local (and locally harmonic) Maaß forms on Grassmanians in certain signatures.

Keywords

higher Siegel theta lift, Eichler–Selberg relations, local Maaß forms, vector-valued mock modular forms

Mathematical Subject Classification

Primary: 11F27

Secondary: 11F37

Milestones

Received: 19 October 2021

Revised: 9 January 2023

Accepted: 5 February 2023

Published: 23 May 2023

Correction: 6 December 2024