a1 Department of Mathematics, Faculty of Science, Okayama University, Okayama 700-8530, Japan (firstname.lastname@example.org)
a2 Department of Mathematics, Sophia University, Tokyo 102-8554, Japan (email@example.com)
a3 Research Institute of Mathematical Science, Kyoto University, Kyoto 606-8502, Japan (firstname.lastname@example.org)
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.
(Received August 24 2008)
(Accepted September 29 2008)
AMS 2010 Mathematics subject classification