2023/01/02 by Zhang, Robin · 1 citation
#11F41 #11F67 (Primary) 11F27 #11F70 #11R27 #11R42 #22E50 (Secondary) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2301.00570
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.