Sarah Peluse

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math.NT2024

Polynomial progressions in topological fields

Ben Krause, Mariusz Mirek, Sarah Peluse +1

Let $P_{1}, \dots, P_{m} \in K [y]$ be polynomials with distinct degrees, no constant terms and coefficients in a general locally compact topological field $K$ . We give a quantitative…

math.NT2024

Bounds in a popular multidimensional nonlinear Roth theorem

Sarah Peluse, Sean Prendiville, Xuancheng Shao

A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$ , $x + d$ , $x + d^{2}$ . We obtain a multidimensional version of this result…