VOL. 84 | 2020 An overview and supplements to the theory of functional relations for zeta-functions of root systems
Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Adv. Stud. Pure Math., 2020: 263-295 (2020) DOI: 10.2969/aspm/08410263


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.


Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283188

Digital Object Identifier: 10.2969/aspm/08410263

Primary: 11M41
Secondary: 11B68 , 11F27 , 11M32 , 11M99

Keywords: Bernoulli functions , Functional relations , Weyl groups , Zeta-functions of root systems

Rights: Copyright © 2020 Mathematical Society of Japan


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