An inverse theorem for higher-degree Davenport constants over prime-power rings
Year: 2026
Type: preprint
Abstract: Let q = p^r and m = p^s, where p is prime and r,s >= 1, and put D = m(q-1). We give a candidate proof that a sequence over Z/qZ of length at least D+1, whose mth elementary symmetric sum is nonzero on every selected subsequence of size between m and D, must be constant at a unit. This implies the inverse classification asked for by Caro, Girard and Schmitt at the extremal length mq-1. The initial modulo-p step refines their Baker-Schmidt parity method at its degree boundary. The proposed contribution is a coefficient comparison that lifts agreement through successive p-adic digits. The principal results retain candidate status.
Author: Barritz, Robert
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223872887