A variation of multiple $L$-values arising from the spectral zeta function of the non-commutative harmonic oscillator

TL;DR

This paper introduces a new variation of multiple L-values linked to the spectral zeta function of a non-commutative harmonic oscillator, providing explicit evaluations through gamma functions in special cases.

Contribution

It defines a novel variation of multiple L-values derived from spectral zeta functions and expresses their generating functions explicitly using gamma functions.

Findings

Generated explicit evaluations of the new L-values in special cases.

Expressed generating functions in terms of gamma functions.

Connected spectral zeta functions with multiple L-values.

Abstract

A variation of multiple $L$-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function can be written in terms of the gamma functions. This result enables us to obtain explicit evaluations of them.