On the Siegel-weil Formula for Quaternionic Unitary Groups
نویسنده
چکیده
We extend the Siegel-Weil formula to all quaternion dual pairs. Applications include the classification problem of skew hermitian forms over a quaternion algebra over a number field and a product formula for the weighted average of the representation numbers of a skew hermitian form by another skew hermitian form.
منابع مشابه
A Simple Case of Siegel-Weil Formula
• The theta correspondence 1 is a correspondence between automorphic forms on two members of a dual reductive pair. Because of the relation between automorphic forms and automor-phic representations, it is also a correspondence between automorphic representations. The Siegel-Weil formula says that certain natural linear combinations of theta lifts are Siegel-type holomorphic Eisenstein Series.
متن کاملPeriods and Special Values of L-functions
Introduction 1 1. Modular forms, congruences and the adjoint L-function 2 2. Quaternion algebras and the Jacquet-Langlands correspondence 6 3. Integral period relations for quaternion algebras over Q 8 4. The theta correspondence 12 5. Arithmetic of the Shimizu lift and Waldspurger’s formula 16 6. Hilbert modular forms, Shimura’s conjecture and a refined version 19 7. Unitary groups and Harris’...
متن کاملQuasi-parabolic Siegel Formula
The result of Siegel that the Tamagawa number of SLr over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the betti numbers of the moduli of parabolic vector bundles using the Weil conjucture.
متن کاملProof of a simple case of the Siegel-Weil formula
On the other hand, while current technique is arguably much more sophisticated, the questions addressed are commensurately more complicated, so that simplification of a proof of a basic Siegel-Weil formula may get lost in more difficult issues. For example, the work of Kudla-Rallis on regularization addresses much more delicate questions than the simple equality of holomorphic Eisenstein series...
متن کامل2 5 Ju n 20 09 On the Siegel - Weil Theorem for Loop Groups ( II ) Howard Garland
This is the second of our two papers on the Siegel-Weil theorem for loop groups. In the first paper [3] we proved the Siegel-Weil theorem for (finite dimensional) snt-modules ([3], Theorem 8.1). In the present paper we use this result to obtain the Siegel-Weil theorem for loop groups, Theorem 7.5, below. In addition to the corresponding result for snt-modules, our proof depends on a convergence...
متن کامل