ON <i>q</i>-ANALOGUES OF ZETA FUNCTIONS OF ROOT SYSTEMS
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- KATO Masaki
- Department of General Education National Institute of Technology Toyama College
Abstract
<p>Komori, Matsumoto and Tsumura introduced a zeta function ζr (s, Δ) associated with a root system Δ. In this paper, we introduce a q-analogue of this zeta function, denoted by ζr (s, a, Δ; q), and investigate its properties. We show that a ‘Weyl group symmetric' linear combination of ζr (s, a, Δ; q) can be written as a multiple integral over a torus involving functions Ψs. For positive integers k, functions Ψk can be regarded as q-analogues of the periodic Bernoulli polynomials. When Δ is of type A2 or A3, the linear combinations can be expressed as the functions Ψk, which are q-analogues of explicit expressions of Witten's volume formula. We also introduce a two-parameter deformation of the zeta function ζr (s, Δ) and study its properties.</p>
Journal
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- Kyushu Journal of Mathematics
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Kyushu Journal of Mathematics 76 (2), 451-475, 2022
Faculty of Mathematics, Kyushu University
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Details 詳細情報について
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- CRID
- 1390856660872280704
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- ISSN
- 18832032
- 13406116
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- KAKEN
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- Abstract License Flag
- Disallowed