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Статья

Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields

Designs, Codes and Cryptography. 2019. Vol. 87. No. 2-3. P. 517-525.
Ballet S., Zykin A. I.

We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field FpFp or Fp2Fp2 where p denotes a prime number ≥5≥5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over Fp2Fp2 attaining the Drinfeld–Vladuts bound and on the descent of these families to the definition field FpFp. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (Funct Approx Commmentarii Math, 55(2):177–197, 2016).