Generalized Bump-Hoffstein conjecture for coverings of the general linear groups

TL;DR

This paper explores the potential generalization of the Bump-Hoffstein conjecture to central coverings of general linear groups, providing evidence through proofs of specific cases.

Contribution

It introduces a generalized form of the Bump-Hoffstein conjecture for coverings of linear groups and proves some special cases to support this extension.

Findings

Evidence supporting the generalized conjecture

Proofs of specific cases of the conjecture

Insights into coverings of linear groups

Abstract

In this paper, we investigate the extent to which the Bump-Hoffstein conjecture could be generalized for central coverings of general linear groups. We provide evidence for such generalized Bump-Hoffstein conjecture by proving some special cases.