Twisted arithmetic Siegel Weil formula on X0(N)
نویسندگان
چکیده
منابع مشابه
Some Extensions of the Siegel-weil Formula
In this article I will survey some relatively recent joint work with S.Rallis, in which we extend the classical formula of Siegel and Weil. In the classical case, this formula identifies a special value of a certain Eisenstein series as an integral of a theta function. Our extension identifies the residues of the (normalized) Eisenstein series on Sp(n) as ‘regularized’ integrals of theta functi...
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• 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.
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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.
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...
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In this article we derive a generalization of the Riemann-Siegel asymptotic formula for the Riemann zeta function. By subtracting the singularities closest to the critical point we obtain a significant reduction of the error term at the expense of a few evaluations of the error function. We illustrate the efficiency of this method by comparing it to the classical Riemann-Siegel formula.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.04.024