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arXiv · 1304.0043

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

Stéphane Ballet·Jean Chaumine·Julia Pieltant
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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 $\F_q$.

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Stéphane Ballet, Jean Chaumine, Julia Pieltant. 2013-03-29. Shimura modular curves and asymptotic symmetric tensor rank of multiplication in any finite field. https://doi.org/10.1007/978-3-642-40663-8_16

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