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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.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…