18 citations · 19 across the 2 of their papers we have counts for
6 papers · 1 filter
Modular forms and arithmetic geometry
Stephen S. Kudla
This article describes results of joint work with Michael Rapoport and Tonghai Yang. First, we construct an modular form ϕ(τ) of weight 3/2 valued in the arithmetic Chow group of t…
Derivatives of Eisenstein series and arithmetic geometry
Stephen S. Kudla
We describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties associated to…
On a conjecture of Jacquet
Michael Harris, Stephen S. Kudla
In this note, we prove in full generality a conjecture of Jacquet concerning the nonvanishing of the triple product L-function at the central point. Let $\kay$ be a number field an…
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…
Integrals of Borcherds forms
Stephen S. Kudla
In his Inventiones papers in 1995 and 1998, Borcherds constructed holomorphic automorphic forms with product expansions on bounded domains associated to rational quadrat…
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…