关于GL$_N$的平衡Voronoï公式

IF 0.5 Q3 MATHEMATICS FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2019-10-28 DOI:10.7169/facm/1810

T. Wong

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引用次数: 2

摘要

S.D.Miller和F.Zhou证明了GL$_N$在$\mathbb Q$上的平衡Voronoi求和公式，它允许控制出现在Voronoi公式两侧的Kloosterman和的维数。在本文中，我们从a.Ichino和N.Templier在数域上的Voronoi求和公式开始，证明了任意数域上一个平衡的Voronai公式，允许在特殊情况下将最近关于谱互易律的结果推广到数域。

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On the balanced Voronoï formula for GL$_N$

S.D. Miller and F. Zhou have proved a balanced Voronoi summation formula for GL$_N$ over $\mathbb Q$, which allows one to control the dimensions of the Kloosterman sums appearing on either side of the Voronoi formula. In this note, we prove a balanced Voronoi formula over an arbitrary number field, starting with the Voronoi summation formula of A. Ichino and N. Templier over number fields, allowing one to extend recent results on spectral reciprocity laws to number fields, in special cases.

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