Symmetries of Rational Functions Arising in Ecalle’s Study of Multiple Zeta Values

  • Adriana Salerno
  • Damaris Schindler
  • Amanda Tucker
Conference paper
Part of the Association for Women in Mathematics Series book series (AWMS, volume 2)


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.



We would like to express our sincerest thanks to our group leader, Leila Schneps, for all of her help and support and for suggesting such an intriguing problem. We would also like to thank the conference organizers of “Women in Numbers—Europe 2013” for all their hard work planning, funding, running, and following up on the wonderful conference that provided us with such a stimulating work environment.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Adriana Salerno
    • 1
  • Damaris Schindler
    • 2
  • Amanda Tucker
    • 3
  1. 1.Mathematics DepartmentBates CollegeLewistonUSA
  2. 2.Hausdorff Center for MathematicsUniversity of BonnBonnGermany
  3. 3.Department of MathematicsState University of New York College at GeneseoGeneseoUSA

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