论文信息 - Some sum-product estimates in matrix rings over finite fields

Some sum-product estimates in matrix rings over finite fields

We study some sum-product problems over matrix rings. Firstly, for A,B,C ⊆ Mn(Fq), we have |A+BC| & q 2 , whenever |A||B||C| & q 2− 2 . Secondly, if a set A in Mn(Fq) satisfies |A| ≥ C(n)q n−1 for some sufficiently large C(n), then we have max{|A+A|, |AA|} & min { |A|2 q 2− 4 , q 2/3|A|2/3 } . These improve the results due to The and Vinh (2020), and generalize the results due to Mohammadi, Pham, and Wang (2021). We also give a new proof for a recent result due to The and Vinh (2020). Our method is based on spectral graph theory and linear algebra.

Gennian Ge | Chengfei Xie | G. Ge | Chengfei Xie

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