Weyl Group Multiple Dirichlet Series III: Eisenstein Series and Twisted Unstable Ar
Weyl Group Multiple Dirichlet Series III: Eisenstein Series and Twisted Unstable Ar
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韦尔群多重狄利克雷级数 III：爱森斯坦级数和扭曲不稳定 Ar
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
J. Hoffstein
中科院分区：
文献类型：
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作者：
Ben Brubaker;D. Bump;S. Friedberg;J. Hoffstein
由Brubaker，Bump，Chinta，Friedberg和Hostein[3]以及Brubaker，Bump和Friedberg[4]给出的Weyl群多重Dirichlet级数与一个根系统和一个包含n次单位根的数域F相联系，只要n是真大的，它们的余项涉及n阶高斯和.N小的情况比较困难，本文讨论了当=Ar时的情形。考虑了包含文[4]的级数作为特例的“扭曲”Dirichet级数。这些级数不是欧拉乘积，但由于它们分量的扭曲乘性，它们是由它们的p-部分决定的。P-部分是由严格的Gelfand-Tsetlin模式参数化的Gauss和的乘积和。猜想这两个重Dirichlet级数是GLR+1的n重亚辛覆盖上的Eisenstein级数的Whittaker等价，并证明了当r=2或n=1时，我们的定义与Chinta[11]在n=2和r6 5时的定义等价.
Weyl group multiple Dirichlet series were associated with a root system and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hostein [3] and Brubaker, Bump and Friedberg [4] provided n is suciently large; their coecients involve n-th order Gauss sums. The case where n is small is harder, and is addressed in this paper when = Ar. “Twisted” Dirichet series are considered, which contain the series of [4] as a special case. These series are not Euler products, but due to the twisted multiplicativity of their coecients, they are determined by their p-parts. The p-part is given as a sum of products of Gauss sums, parametrized by strict Gelfand-Tsetlin patterns. It is conjectured that these multiple Dirichlet series are Whittaker coecients of Eisenstein series on the n-fold metaplectic cover of GLr+1, and this is proved if r = 2 or n = 1. The equivalence of our definition with that of Chinta [11] when n = 2 and r 6 5 is also established.