the class number formula describes the behavior of the dedekind zeta function at s = 0 and s = 1. the stark and gross conjectures extend the class number formula, describing the behavior of artin l-functions and p-adic l-functions at s = 0 and s = 1 in terms of units. the harris–venkatesh conjecture describes the residue of stark units modulo p, giving a modular analogue to the stark and gross conjectures while also serving as the first verifiable part of the broader conjectures of venkatesh, prasanna, and galatius.
in this talk, i will draw an introductory picture, formulate a unified conjecture combining harris–venkatesh and stark for weight one modular forms, and describe the proof of this in the imaginary dihedral case.