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Number Theory Seminar

Thursday, February 2, 2023
4:00pm to 5:00pm
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Linde Hall 387
The Gross--Kohnen--Zagier formula via $p$-adic uniformisation
Lea Beneish, Department of Mathematics, UC Berkeley,

The Gross-Kohnen-Zagier theorem says that certain generating series of CM points are modular forms of weight 3/2 in the Jacobian of the modular curve $X_0(N)$. In this talk, I will discuss a new proof of the Gross--Kohnen--Zagier formula for Shimura curves which uses the $p$-adic uniformisation of Cerednik--Drinfeld. The explicit description of CM points via this uniformisation leads to an expression for the Gross--Kohnen--Zagier generating series as the ordinary projection of the first derivative of a $p$-adic family of positive definite ternary theta series. This is joint work with Henri Darmon, Lennart Gehrmann and Marti Roset Julia.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].