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• W2964093395 abstract "We present effective upper bounds on the symmetric bilinear complexity of multiplication in extensions of a base finite field $$mathbb {F}_{p^2}$$ of prime square order, obtained by combining estimates on gaps between prime numbers together with an optimal construction of auxiliary divisors for multiplication algorithms by evaluation-interpolation on curves. Most of this material dates back to a 2011 unpublished work of the author, but it still provides the best results on this topic at the present time. Then a few updates are given in order to take recent developments into account, including comparison with a similar work of Ballet and Zykin, generalization to classical bilinear complexity over $$mathbb {F}_p$$ , and to short multiplication of polynomials, as well as a discussion of open questions on gaps between prime numbers or more generally values of certain arithmetic functions." @default.
• W2964093395 created "2019-07-30" @default.
• W2964093395 creator A5055564070 @default.
• W2964093395 date "2018-11-19" @default.
• W2964093395 modified "2023-10-01" @default.
• W2964093395 title "Gaps between prime numbers and tensor rank of multiplication in finite fields" @default.
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• W2964093395 doi "https://doi.org/10.1007/s10623-018-0584-0" @default.
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