Will Sawin

collaborators

7 papers

math.NT2026

The asymptotic in Waring's problem over function fields via a singular locus in the circle method

Will Sawin

We give results on the asymptotic in Waring's problem over function fields that are stronger than the results obtained over the integers using the main conjecture in Vinogradov's m…

math.NT2026

Distributions of unramified extensions of global fields

Will Sawin, Melanie Matchett Wood

Given a finite group $I^$ , we prove results on the distribution of the prime-to- $q ∣ I^∣$ part of fundamental groups of $I^$ -covers of the projective line $P_{F_{q}}^{1}$ …

math.NT2026

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…

math.NT2026

Counting number fields of fixed degree by their smallest defining polynomial

Santiago Arango-PiÃ±eros, Fabian Gundlach, Robert J. Lemke Oliver +5

When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of $GL_{2} \times GL_{1}$ on the space of polynom…

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.AG2025

Big monodromy for higher Prym representations

Aaron Landesman, Daniel Litt, Will Sawin

Let $I^£_{g^{'}} \to I^£_{g}$ be a cover of an orientable surface of genus g by an orientable surface of genus g', branched at n points, with Galois group H. Such a cover induces a virtual…