3 papers
math.NT2026
A higher Gross-Zagier type formula for moduli of shtukas at deeper level
Patrick Bieker
We generalize the function field analogue analogue of the Gross-Zagier and Waldspurger formulae due to Yun and Zhang relating the (higher) derivative of an automorphic (base change…
math.AG2025
Normality of Schubert varieties in affine Grassmannians II: The tamely ramified case
Patrick Bieker
We prove a criterion for the normality of Schubert varieties in twisted affine Grassmannians in terms of the order of the algebraic fundamental group of a certain Levi subgroup, in…
math.NT2024
A converse theorem for Borcherds products in signature
Patrick Bieker, Paul Kiefer
We show that a modular unit on two copies of the upper half-plane is a Borcherds product if and only if its boundary divisor is a special boundary divisor. Therefore, we define a s…