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Twisted Borcherds products on Hilbert modular surfaces and their CM values
Jan Hendrik Bruinier, Tonghai Yang
We construct a natural family of rational functions on a Hilbert modular surface from the classical -invariant and its Hecke translates. These functions are obtained…
Derivatives of Eisenstein series and Faltings heights
S. Kudla, M. Rapoport, T. Yang
We prove a relation between a generating series for the heights of Heegner cycles on the arithmetic surface associated to a Shimura curve and the second term in the Laurent expansi…
Non-vanishing of the Central Derivative of Canonical Hecke L-functions
Stephen D. Miller, Tonghai Yang
In the early 1980s, Rohrlich began a study of canonical Hecke characters, which are closely related to the simplest examples of CM elliptic curves. He and Montgomery showed the non…
A peculiar modular form of weight one
Stephen S. Kudla, Michael Rapoport, Tonghai Yang
In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious p…