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The Tamely Ramified Geometric Quantitative Minimal Ramification Problem
Mark Shusterman
We prove a large finite field version of the Boston--Markin conjecture on counting Galois extensions of the rational function field with a given Galois group and the smallest possi…
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…
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…
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…
Squarefree polynomials with prescribed coefficients
Amotz Oppenheim, Mark Shusterman
For nonempty subsets of a (large enough) finite field satisfying …