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Uniform nonlinear Szemer\'{e}di theorem for corners in finite fields
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Uniform nonlinear Szemer\'{e}di theorem for corners in finite fields
abstract
Let $P(t),Q(t)\in \mathbb{Q}(t)$ be rational functions such that $P(t),Q(t)$ and the constant function $1$ are linearly independent over $\mathbb{Q}$, we prove an asymptotic formula for the number of the corner configurations $(x_1,x_2),(x_1+P(y),x_2),(x_1,x_2+Q(y))$ in the subsets of $\mathbb{F}_p^2$.
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Cited by 1 Pith paper
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