Published In
Ramanujan Journal
Document Type
Pre-Print
Publication Date
11-5-2025
Subjects
Modular forms, Hecke operators, Trace formulas
Abstract
The expectation that Ramanujan’s tau function does not vanish, commonly known as Lehmer’s Conjecture, has inspired several extensions to broader settings. In this paper, we focus on one such direction, proposed by Rouse, concerning the non-vanishing of traces of Hecke operators Tn. We refine an algorithm originally introduced by Rouse to resolve the case n = 2, and, together with tools from our earlier work on the case n = 3 in level one, we settle the conjecture for T3 in full generality. We also discuss an implication of our result for the non-vanishing of all coefficients of the characteristic polynomial of T3.
Rights
© Copyright the author(s) 2025
DOI
10.1007/s11139-025-01235-y
Persistent Identifier
https://archives.pdx.edu/ds/psu/44256
Publisher
Springer Science and Business Media LLC
Citation Details
Chiriac, L., & Williams, E. (2025). A generalized Lehmer conjecture for the trace of T3. The Ramanujan Journal, 68(3).
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: A generalized Lehmer conjecture for the trace of T3. The Ramanujan Journal, 68(3).