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5 papers
Möbius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields
Will Sawin, Mark Shusterman
We establish cancellation in short sums of certain special trace functions over below the Pólya-Vinogradov range, with savings approaching square-root cancellatio…
The Hanna Neumann conjecture for Demushkin Groups
Andrei Jaikin-Zapirain, Mark Shusterman
We confirm the Hanna Neumann conjecture for topologically finitely generated closed subgroups and of a nonsolvable Demushkin group . Namely, we show that \begin{equation…
Balanced presentations for fundamental groups of curves over finite fields
Mark Shusterman
We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed…
Squarefree polynomials with prescribed coefficients
Amotz Oppenheim, Mark Shusterman
For nonempty subsets of a (large enough) finite field satisfying …
Virtual retraction and Howson's theorem in pro- groups
Mark Shusterman, Pavel Zalesskii
We show that for every finitely generated closed subgroup of a non-solvable Demushkin group , there exists an open subgroup of containing , and a continuous homom…