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pro vyhledávání: '"A, Millson"'
In the 80's Kudla and Millson introduced a theta function in two variables. It behaves as a Siegel modular form with respect to the first variable, and is a closed differential form on an orthogonal Shimura variety with respect to the other variable.
Externí odkaz:
http://arxiv.org/abs/2406.19921
Autor:
Metzler, Ingmar, Zuffetti, Riccardo
Let $L$ be an even indefinite lattice. We show that if $L$ splits off a hyperbolic plane and a scaled hyperbolic plane, then the Kudla-Millson lift of genus $1$ associated to $L$ is injective. Our result includes as special cases all previously known
Externí odkaz:
http://arxiv.org/abs/2312.00572
Autor:
Branchereau, Romain
Let $V$ be quadratic space of even dimension and of signature $(p, q)$ with $p \geq q > 0$. We show that the Kudla-Millson lift of toric cycles - attached to algebraic tori - is a cusp form that is the diagonal restriction of a Hilbert modular form o
Externí odkaz:
http://arxiv.org/abs/2401.16996
Autor:
Stein, Oliver
We prove a converse theorem for the multiplicative Borcherds lift for lattices of square-free level whose associated discriminant group is anisotropic. This can be seen as generalization of Bruinier's results in \cite{Br2}, which provides a converse
Externí odkaz:
http://arxiv.org/abs/2306.17660
Autor:
Kiefer, Paul, Zuffetti, Riccardo
We study the injectivity of the Kudla-Millson lift of genus 2 Siegel cusp forms, vector-valued with respect to the Weil representation associated to an even lattice L. We prove that if L splits off two hyperbolic planes and is of sufficiently large r
Externí odkaz:
http://arxiv.org/abs/2307.15809
Autor:
García, Luis E.
We consider arbitrary polarized variations of Hodge structure of weight two and $h^{2,0}=1$ over a non--singular complex algebraic curve $S$ and analyze the boundary behaviour of the associated Kudla--Millson theta series using Schmid's theorems on d
Externí odkaz:
http://arxiv.org/abs/2301.08733
Autor:
Branchereau, Romain
In \cite{km2}, Kudla and Millson constructed a $q$-form $\varphi_{KM}$ on an orthogonal symmetric space using Howe's differential operators. It is a crucial ingredient in their theory of theta lifting. This form can be seen as a Thom form of a real o
Externí odkaz:
http://arxiv.org/abs/2211.10341
Autor:
Branchereau, Romain
We consider the Kudla-Millson theta series associated to a quadratic space of signature $(N,N)$. By combining a `see-saw' argument with the Siegel-Weil formula, we show that its (regularized) integral along a torus attached to a totally real field of
Externí odkaz:
http://arxiv.org/abs/2211.11698
Autor:
Zuffetti, Riccardo
Publikováno v:
Math. Z., vol. 307, no. 10 (2024)
We unfold the theta integrals defining the Kudla-Millson lift of genus 1 associated to even lattices of signature (b,2), where b>2. This enables us to compute the Fourier expansion of such defining integrals and prove the injectivity of the Kudla-Mil
Externí odkaz:
http://arxiv.org/abs/2206.05079
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