Simultaneous popular polynomial differences hold over large F_p for linearly independent zero-constant polynomials, but fail for paired 3-APs over F_p^n as n grows.
Duke Math
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Simultaneous popular polynomial differences over finite fields
Simultaneous popular polynomial differences hold over large F_p for linearly independent zero-constant polynomials, but fail for paired 3-APs over F_p^n as n grows.