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

2017/06/28 by Ballet, Stéphane, Zykin, Alexey
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.09139

Abstract

We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp or Fp2 where p denotes a prime number greater or equal than 5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over Fp2 attaining the Drinfeld-Vladuts bound and on the descent of these families to the definition field Fp. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (2016).

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