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 and class numbers. 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 Prasanna–Venkatesh conjectures. In this talk, I will draw a 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.

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