Arithmetic mixed Siegel-Weil formulas and modular form of arithmetic divisors

Abstract: The classical Siegel–Weil formula relates theta series to Eisenstein series and its arithmetic version is central in Kudla's program. I will discuss arithmetic mixed Siegel-Weil formulas. I will focus on the one in the work of Gross and Zagier, and the one in my recent work. As an application, I obtained modular generating series of arithmetic extensions of Kudla's special divisors for unitary Shimura varieties over CM fields with arbitrary split level. This provides a partial solution to a problem of Kudla.

algebraic geometrynumber theory

Audience: researchers in the topic

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MIT number theory seminar

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