Sums of Two-Parameter Deformations of Multiple Polylogarithms

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2021-10-08 DOI:10.1007/s11040-021-09407-0

Masaki Kato

引用次数: 1

Abstract

In this paper, we introduce a generating function of sums of two-parameter deformations of multiple polylogarithms, denoted by Φ₂(a;p,q), and study a q-difference equation satisfied by it. We show that this q-difference equation can be solved by expanding Φ₂(a;p,q) into power series of the parameter p and then using the method of variation of constants. By letting \(p \rightarrow 0\) in the main theorem, we find that the generating function of sums of q-interpolated multiple zeta values can be written in terms of the q-hypergeometric function ₃ϕ₂, which is due to Li-Wakabayashi.

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多个多对数的双参数变形和

本文引入了一个多对数双参数变形和的生成函数Φ2(a;p,q)，并研究了它所满足的q差分方程。我们证明了将Φ2(a;p,q)展开为参数p的幂级数，然后用变分常数的方法可以求解这个q-差分方程。通过将\(p \rightarrow 0\)代入主要定理，我们发现q插值的多个zeta值的和的生成函数可以用q超几何函数3ϕ2表示，这是由Li-Wakabayashi提出的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.