The Harris-Venkatesh conjecture for derived Hecke operators I: imaginary dihedral forms
Number Theory
2023-05-24 v2
Abstract
The Harris-Venkatesh conjecture posits a relationship between the action of derived Hecke operators on weight-one modular forms and Stark units. We prove the full Harris-Venkatesh conjecture for imaginary dihedral weight-one modular forms. This reproves results of Darmon-Harris-Rotger-Venkatesh, extends their work to the adelic setting, and removes all assumptions on primality and ramification from the imaginary dihedral case of the Harris-Venkatesh conjecture. This is accomplished by introducing two new key ingredients: the Harris--Venkatesh period on modular curves and the two-variable optimal form.
Keywords
Cite
@article{arxiv.2301.00570,
title = {The Harris-Venkatesh conjecture for derived Hecke operators I: imaginary dihedral forms},
author = {Robin Zhang},
journal= {arXiv preprint arXiv:2301.00570},
year = {2023}
}
Comments
51 pages, some auxiliary material moved to the sequels arXiv:2305.08956 and arXiv:2301.00612