MIT Number Theory Seminar

Tuesday, September 12, 2023 at 4:30pm to 5:30pm

MIT, 2-449 182 Memorial Drive, Cambridge, MA 02142

Speakers:  Robin Zhang (MIT)

Title:  Harris–Venkatesh plus Stark

Abstract:  The class number formula describes the behavior of the Dedekind zeta function at = 0 and = 1. The Stark and Gross conjectures extend the class number formula, describing the behavior of Artin L-functions and p-adic L-functions at = 0 and = 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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Bjorn Poonen, Number Theory Seminar, Number_Theory_Seminar, Wei Zhang, Andrew Sutherland


Department of Mathematics


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