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Harmonic and equianharmonic equations in the Grothendieck–Teichmüller group. III

  • Hiroaki Nakamura (a1), Hiroshi Tsunogai (a2) and Seidai Yasuda (a3)

Abstract

We study behaviours of the ‘equianharmonic’ parameter of the Grothendieck–Teichmüller group introduced by Lochak and Schneps. Using geometric construction of a certain one-parameter family of quartics, we realize the Galois action on the fundamental group of a punctured Mordell elliptic curve in the standard Galois action on a specific subgroup of the braid group . A consequence is to represent a matrix specialization of the ‘equianharmonic’ parameter in terms of special values of the adelic beta function introduced and studied by Anderson and Ihara.

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