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September 5, 2025Monatshefte für Mathematik0 citationsOpen Access

Symmetric sum formula for elliptic q-multiple polylogarithms

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MKMasaki Kato

Key Points

  • The paper generalizes symmetric sum formulas to elliptic q-multiple polylogarithms, highlighting analytical relationships.
  • It establishes an inversion formula for the generalized symmetric sum, connecting multiple zeta values and elliptic forms.
  • Hoffman's previous work is foundational, as it relates these elliptic forms back to Riemann zeta values effectively.
  • The exploration of these relationships might open new pathways in the understanding of complex analytical connections in number theory.

Abstract

Abstract Hoffman 11 showed that certain symmetric sums of multiple zeta star values can be written in terms of Riemann zeta values. In this paper, we consider generalization of this symmetric sum formula to elliptic q -multiple polylogarithms, which are common deformations of q - and elliptic multiple polylogarithms. We also establish an inversion formula of the generalized formula and investigate the relationship between the sum formulas satisfied by multiple zeta values and it.

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Cite This Study

Masaki Kato (2025) studied this question.

synapsesocial.com/papers/68bb42142b87ece8dc9585b0https://doi.org/10.1007/s00605-025-02106-w
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