Abstract
We obtain new asymptotical bounds for the symmetric tensor rank of multiplication in any finite extension of any finite field \(\mathbb{F}_q\). In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on a family of Shimura modular curves defined over \(\mathbb{F}_{q^2}\) attaining the Drinfeld-Vlăduţ bound and on the descent of this family over the definition field \(\mathbb{F}_q\).
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Ballet, S., Chaumine, J., Pieltant, J. (2013). Shimura Modular Curves and Asymptotic Symmetric Tensor Rank of Multiplication in any Finite Field. In: Muntean, T., Poulakis, D., Rolland, R. (eds) Algebraic Informatics. CAI 2013. Lecture Notes in Computer Science, vol 8080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40663-8_16
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DOI: https://doi.org/10.1007/978-3-642-40663-8_16
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