q-Multiple Zeta Functions and q-Multiple Polylogarithms

Abstract

We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.

24 pages. We add a section on q-iterated integral shuffle relations of q-multiple zeta values. We also correct some typos

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• q-Multiple Zeta Functions and q-Multiple Polylogarithms
• Special functions and q-commuting variables
• A q-analog of Euler's decomposition formula for the double zeta function
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Cited by in corpus (35)

• Multiple $q$-Zeta Values
• q-Multiple Zeta Functions and q-Multiple Polylogarithms
• Duality for Finite Multiple Harmonic q-Series
• q-Hardy-Berndt type sums associated with q-Genocchi type zeta and l-functions
• Cyclotomic analogues of finite multiple zeta values
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function
• Integral representations of q-analogues of the Hurwitz zeta function
• Large $N$ and large representations of Schur line defect correlators
• The Algebra of a q-Analogue of Multiple Harmonic Series
• Evaluations of multiple Dirichlet $L$-values via symmetric functions
• Unfolding the double shuffle structure of q-multiple zeta values
• Renormalization of Multiple $q$-Zeta Values
• Heat trace and spectral action on the standard Podles sphere
• Duality and (q-)multiple zeta values
• On Euler's decomposition formula for qMZVs
• Explicit double shuffle relations and a generalization of Euler's decomposition formula
• On $q$-Analogs of Some Families of Multiple Harmonic Sum and Multiple Zeta Star Value Identities
• The algebra of generating functions for multiple divisor sums and applications to multiple zeta values
• Renormalisation of q-regularised multiple zeta values
• Identity Families of Multiple Harmonic Sums and Multiple Zeta (Star) Values
• Derivations on the algebra of multiple harmonic q-series and their applications
• Uniform Approach to Double Shuffle and Duality Relations of Various q-Analogs of Multiple Zeta Values via Rota-Baxter Algebras
• On $q$-analogues of two-one formulas for multiple harmonic sums and multiple zeta star values
• Rota--Baxter algebras and left weak composition quasi-symmetric functions
• Finite and symmetric Mordell-Tornheim multiple zeta values
• Balanced multiple q-zeta values
• A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values
• q-deformations of statistical mechanical systems and motives over finite fields
• Quadratic relations for a q-analogue of multiple zeta values
• On q-Analog of Wolstenholme Type Congruences for Multiple Harmonic Sums
• Topological properties of $q$-analogues of multiple zeta values
• A unified approach to qMZVs
• Sum of interpolated multiple $q$-zeta values
• On q-analogues of quadratic Euler sums