##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Robin Zhang

#### MIT

## Harris–Venkatesh plus Stark

##### Abstract:

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.

### November 9, 2023

### 12:40 PM

APM 6402 and Zoom

See https://www.math.ucsd.edu/~nts

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