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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Symmetries of Rational Functions Arising in Ecalle’s Study of Multiple Zeta Values
verfasst von : Adriana Salerno, Damaris Schindler, Amanda Tucker
Erschienen in: Women in Numbers Europe
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Abstract
In Ecalle’s theory of multiple zeta values he makes frequent use of certain properties that express symmetries of rational functions in several variables. We focus on the properties of \(\mathop{\mathrm{push}}\nolimits\)-invariance, \(\mathop{\mathrm{circ}}\nolimits\)-neutrality, and alternality. Ecalle states and uses several implications about the relations between these symmetries. In this paper we investigate two of these implications and prove two results: first, that \(\mathop{\mathrm{push}}\nolimits\)-invariance and \(\mathop{\mathrm{circ}}\nolimits\)-neutrality imply the first alternality relation, but not the more general alternality relations, and second, that alternality does, indeed, imply \(\mathop{\mathrm{circ}}\nolimits\)-neutrality.