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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…
On the Chowla and twin primes conjectures over
Will Sawin, Mark Shusterman
Using geometric methods, we improve on the function field version of the Burgess bound, and show that, when restricted to certain special subspaces, the Möbius function over $\math…
Semi-free subgroups of a profinite surface group
Matan Ginzburg, Mark Shusterman
We show that every closed normal subgroup of infinite index in a profinite surface group is contained in a semi-free profinite normal subgroup of . This answers a question o…
Irreducibility of polynomials with a large gap
William Sawin, Mark Shusterman, Michael Stoll
We generalize an approach from a 1960 paper by Ljunggren, leading to a practical algorithm that determines the set of such that…