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arXiv · 2503.11955

A generalization of Zwegers' multivariable $\mu$-function

G. Shibukawa·S. Tsuchimi
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Abstract

We introduce a one parameter deformation of Zwegers' multivariable $\mu$-function by applying iterations of the $q$-Borel summation method, which is also a multivariate analogue of the generalized $\mu$-function introduced by the authors. For this deformed multivariable $\mu$-function, we give some formulas, for example, forward shift formula, translation and $\mathfrak{S}_{N+1}$-symmetry. Further we mention modular formulas for the Zwegers' original multivariable $\mu$-function.

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G. Shibukawa, S. Tsuchimi. 2025-03-15. A generalization of Zwegers' multivariable $\mu$-function. https://arxiv.org/abs/2503.11955

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