Proves optimal homological vanishing line for H_i(B_n, V^{\otimes n}) giving power-saving cancellation bounds for Gauss sums and character sums over function fields, extending Patterson's conjecture.
[ES26] Jordan Ellenberg and Mark Shusterman.Averages of Arithmetic Functions over Con- ductors of Function Fields
2 Pith papers cite this work. Polarity classification is still indexing.
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Modifications to Klagsbrun-Mazur-Rubin yield bounds on Selmer rank distributions for Galois modules in p-cyclic extensions ordered by ramified primes, with applications to elliptic curve rank gains and point counts on superelliptic and hyperelliptic curves.
citing papers explorer
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Optimal homological vanishing: cancellation of character sums and Patterson's conjecture over $\mathbb{F}_q[t]$
Proves optimal homological vanishing line for H_i(B_n, V^{\otimes n}) giving power-saving cancellation bounds for Gauss sums and character sums over function fields, extending Patterson's conjecture.
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Distribution of Selmer ranks in prime cyclic extensions
Modifications to Klagsbrun-Mazur-Rubin yield bounds on Selmer rank distributions for Galois modules in p-cyclic extensions ordered by ramified primes, with applications to elliptic curve rank gains and point counts on superelliptic and hyperelliptic curves.