Harris-Venkatesh plus Stark

Robin Zhang, Columbia University
Fine Hall 214

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits.

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 give 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.