25 citations · 132 across the 31 of their papers we have counts for
17 papers · 1 filter
The case of an N-gon
Jens Funke, Stephen Kudla
We construct the indefinite theta series attached to N-gons in the symmetric space of an indefinite inner product space of signature (m-2,2) following the suggestions of section C…
On the subring of special cycles
Stephen Kudla
For a totally real field F of degree d>1 and a quadratic space V of signature (m,2)^{d_+} x (m+2,0)^{d-d_+} with associated Shimura variety Sh(V), we consider the subring of cohomo…
Remarks on generating series for special cycles
Stephen Kudla
In this note, we consider special algebraic cycles on the Shimura variety S associated to a quadratic space V over a totally real field F, |F:\Q|=d, of signature ((m,2)^{d_+},(m+2,…
Modularity of generating series of divisors on unitary Shimura varieties II: arithmetic applications
Jan Bruinier, Benjamin Howard, Stephen S. Kudla +2
We prove two formulas in the style of the Gross-Zagier theorem, relating derivatives of L-functions to arithmetic intersection pairings on a unitary Shimura variety. We also prove…
Theta integrals and generalized error functions, II
Jens Funke, Stephen Kudla
Theta series for indefinite quadratic lattices were introduced by Zwegers, for signature (m-1,1), Alexandrov, Banerjee, Manschot and Pioline, for signature (m-2,2), and Nazaroglu,…
Modularity of generating series of divisors on unitary Shimura varieties
Jan Bruinier, Benjamin Howard, Stephen S. Kudla +2
We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a un…
A classification of harmonic Maass forms
Kathrin Bringmann, Stephen Kudla
We give a classification of the Harish-Chandra modules generated by the pullback to of harmonic Maass forms for congruence subgroups of $\text{SL}_2(\mathb…
Theta integrals and generalized error functions
Stephen Kudla
In a recent preprint, arXiv:1606.05495v1, Alexandrov, Banerjee, Manschot and Pioline introduced generalized error functions and used them to construct indefinite theta series assoc…
An alternative description of the Drinfeld p-adic half-plane
Stephen Kudla, Michael Rapoport
We show that the Deligne formal model of the Drinfeld p-adic halfplane relative to a non-archimedean local field F represents a moduli problem of polarized O_F-modules with an acti…
On the pullback of an arithmetic theta function
Stephen Kudla, Tonghai Yang
In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space $\Cal C$ of elliptic curves with C…
Faltings heights of big CM cycles and derivatives of L-functions
Jan Hendrik Bruinier, Stephen S. Kudla, Tonghai Yang
We give a formula for the values of automorphic Green functions on the special rational 0-cycles (big CM points) attached to certain maximal tori in the Shimura varieties associate…
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…