Weighted multilinear polynomial averages in finite fields are controlled by the u^(d+1)-norm of the weight, yielding quantitative convergence and new asymptotic formulas for multidimensional rational function progressions of arbitrary length.
Multiple ergodic theorems for arithmetic sets
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On weighted multilinear polynomial averages in finite fields
Weighted multilinear polynomial averages in finite fields are controlled by the u^(d+1)-norm of the weight, yielding quantitative convergence and new asymptotic formulas for multidimensional rational function progressions of arbitrary length.