@inbook{cefd0f8fac84438bb059aca3cdffaa53,
title = "On some bounds for symmetric tensor rank of multiplication in finite fields",
abstract = "The aim of this paper is twofold. On the one hand, we establish new upper bounds for the symmetric multiplication tensor in any extension of finite fields. Note that these bounds are not asymptotic but uniform. On the other hand, we clarify the current state of the art by giving the detailed proof of some known unpublished uniform bounds, and we discuss the validity of some current asymptotic bounds and their relation with the fields of definition of certain Shimura curves.",
keywords = "Algebraic function fields, Finite fields, Shimura curves, Tensor rank of multiplication",
author = "St{\'e}phane Ballet and Julia Pieltant and Matthieu Rambaud and Jeroen Sijsling",
note = "Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",
year = "2017",
month = jan,
day = "1",
doi = "10.1090/conm/686/13779",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "93--121",
booktitle = "Contemporary Mathematics",
}