An overview and supplements to the theory of functional relations for zeta-functions of root systems

机译：概述和补充到根系系统的Zeta函数的功能关系理论

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We give an overview of the theory of functional relations for zeta-functions of root systems, and show some new results on functional relations involving zeta-functions of root systems of types B_r, D_r, A_3 and C_2. To show those new results, we use two different methods. The first method, for B_r, D_r, A_3, is via generating functions, which is based on the symmetry with respect to Weyl groups, or more generally, on our theory of lattice sums of certain hyperplane arrangements. The second method for C_2 is more elementary, using partial fraction decompositions.

机译：我们概述了根系系统Zeta函数的功能关系理论，并对涉及类型B_R，D_R，A_3和C_2的根系统的Zeta函数的功能关系显示一些新的结果。要显示那些新结果，我们使用两种不同的方法。对于B_R，D_R，A_3的第一方法是通过产生功能，其基于对赘囊的对称性，或者更一般地，在我们的晶格和超平面布置的晶格和的理论上。使用部分分数分解，C_2的第二种方法更基本。

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《International Conference "Various Aspects of Multiple Zeta Functions"》|2020年|411 pages :|共33页
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Yasushi Komori; Kohji Matsumoto; Hirofumi Tsumura;
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中图分类 51.415083;
关键词
Zeta-functions of root systems; Functional relations; Weyl groups; Bernoulli functions;

机译：Zeta函数的根系;功能关系;Weyl族;Bernoulli函数;

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2. SOME FUNCTIONAL RELATIONS IN THE DENSITY FUNCTIONAL THEORY OF FINITE INTERACTING ELECTRONIC SYSTEMS [J] . Parr RG., Liu SB. Chemical Physics Letters . 1997,第1a2期

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An overview and supplements to the theory of functional relations for zeta-functions of root systems

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