Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field

Abstract

We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any finite extension of any finite field $\F_q$. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on a family of Shimura modular curves defined over $\F_{q^2}$ attaining the Drinfeld-Vladut bound and on the descent of this family over the definition field $\F_q$.

arXiv admin note: text overlap with arXiv:1107.1184

References in corpus (2)

• Torsion Limits and Riemann-Roch Systems for Function Fields and Applications
• On the existence of non-special divisors of degree $g$ and $g-1$ in algebraic function fields over $\F_q$