M. Shusterman

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math.NT2026

Arithmetic Wu Formulas and the Generalized Hecke Theorem

Shachar Carmeli, Mark Shusterman, Sa'ar Zehavi

We construct canonical Steenrod square operations on the Geisser--Schmidt/Milne modified compactly supported Ã©tale cohomology of separated finite-type schemes over rings of $S$ -in…

math.NT2026

Pro- $ℓ$ -by-cyclotomic and tamely ramified variants of the Neukirch-Uchida Theorem

Ido Karshon, Mark Shusterman

We prove a generalization of the Neukirch-Uchida Theorem. In particular, we show that the isomorphism type of a number field $K$ can be recovered from the maximal pro- $ℓ$ -by-cyc…

math.NT2026

Averages of Arithmetic Functions over Conductors of Function Fields

Jordan Ellenberg, Mark Shusterman

For a finite group $G$ and a sufficiently large (but fixed) prime power $q$ coprime to $G$ we obtain asymptotics for the number of regular Galois extensions $L / F_{q} (t)$ , w…

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…

Arithmetic Wu Formulas and the Generalized Hecke Theorem

Pro-ℓ-by-cyclotomic and tamely ramified variants of the Neukirch-Uchida Theorem

Averages of Arithmetic Functions over Conductors of Function Fields

Short sums of trace functions over function fields and their applications

Pro- $ℓ$ -by-cyclotomic and tamely ramified variants of the Neukirch-Uchida Theorem