Will Sawin

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20242026

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math.NT2025

Short sums of trace functions over function fields and their applications

Will Sawin, Mark Shusterman

For large enough (but fixed) prime powers $q$ , and trace functions to squarefree moduli in $F_{q} [u]$ with slopes at most $1$ at infinity, and no Artin--Schreier factors in…

math.CO2025

The independence and clique cover numbers of the squarefree graph

Boris Alexeev, Dustin G. Mixon, Will Sawin

We determine the largest subset $A \subseteq {1, \dots, n}$ such that for all $a, b \in A$ , the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the comp…

math.NT2025

Functional equations of axiomatic multiple Dirichlet series, Weyl groupoids, and quantum algebra

Will Sawin, Ian Whitehead

We prove functional equations for multiple Dirichlet series defined by a collection of five geometric axioms. We find functional equations of two types: one modeled on the function…