Generating Function of q- and Elliptic Multiple Polylogarithms of Hurwitz Type

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-05-21 DOI:10.1007/s11040-024-09480-1

Masaki Kato

引用次数: 0

Abstract

Ohno and Zagier (Indag Math 12:483–487, 2001) found that a generating function of sums of multiple polylogarithms can be written in terms of the Gauss hypergeometric function \({}_2F_1\). As a generalization of the Ohno and Zagier formula, Ihara et al. (Can J Math 76:1–17, 2022) showed that a generating function of sums of interpolated multiple polylogarithms of Hurwitz type can be expressed in terms of the generalized hypergeometric function \({}_{r+1}F_r\). In this paper, we establish q- and elliptic analogues of this result. We introduce elliptic q-multiple polylogarithms of Hurwitz type and study a generating function of sums of them. By taking the trigonometric and classical limits in the main theorem, we can obtain q- and elliptic generalizations of the Ihara, Kusunoki, Nakamura and Saeki formula.

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赫尔维茨型 q 多项式和椭圆多项式的生成函数

Ohno 和 Zagier (Indag Math 12:483-487, 2001) 发现多重多项式之和的生成函数可以用高斯超几何函数 \({}_2F_1\) 来表示。作为对 Ohno 和 Zagier 公式的推广，Ihara 等人（Can J Math 76:1-17，2022 年）证明了赫维茨型内插多重多项式之和的生成函数可以用广义超几何函数 \({}_{r+1}F_r\)来表示。在本文中，我们建立了这一结果的 q- 和椭圆类比。我们引入了赫尔维茨类型的椭圆 q 多次多项式，并研究了它们之和的生成函数。通过主定理中的三角极限和经典极限，我们可以得到伊原、草木、中村和佐伯公式的q和椭圆广义。

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.