关于根系统的ZETA函数的q-相似性

IF 0.6 4区 数学 Q3 MATHEMATICS
Masakimi Kato
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引用次数: 1

摘要

Komori、Matsumoto和Tsumura引入了与根系(cid:49)相关的ζr(s,(cid:49))函数。在本文中,我们引入了这个ζ函数的q-类似物,表示为ζr(s,a,(cid:49);q),并研究其性质。我们证明了ζr(s,a,(cid:49)的“Weyl群对称”线性组合;q)可以写成包含函数ψs的环面上的多重积分。对于正整数k,函数ψk可以看作周期伯努利多项式的q-类似物。当(cid:49)是A2或A3型时,线性组合可以表示为函数ψk,它是Witten体积公式显式表达式的q-类似物。我们还引入了ζr(s,(cid:49))的双参数变形,并研究了它的性质,
本文章由计算机程序翻译,如有差异,请以英文原文为准。
ON q-ANALOGUES OF ZETA FUNCTIONS OF ROOT SYSTEMS
. Komori, Matsumoto and Tsumura introduced a zeta function ζ r ( s , (cid:49)) associated with a root system (cid:49) . In this paper, we introduce a q -analogue of this zeta function, denoted by ζ r ( s , a , (cid:49) ; q ) , and investigate its properties. We show that a ‘Weyl group symmetric’ linear combination of ζ r ( s , a , (cid:49) ; q ) can be written as a multiple integral over a torus involving functions ψ s . For positive integers k , functions ψ k can be regarded as q -analogues of the periodic Bernoulli polynomials. When (cid:49) is of type A 2 or A 3 , the linear combinations can be expressed as the functions ψ k , which are q -analogues of explicit expressions of Witten’s volume formula. We also introduce a two-parameter deformation of the zeta function ζ r ( s , (cid:49)) and study its properties. ,
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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