Polynomial configurations in sets of positive upper density over local fields

Mohammad Bardestani, Keivan Mallahi-Karai

Let $F(x)=(f_1(x),\dots ,f_m(x))$ be such that $1,f_1,\dots ,f_m$ are linearly independent polynomials with real coefficients. Based on ideas of Bachoc, DeCorte, Oliveira and Va…