Published October 27, 2026 | Version 1

An inverse theorem for higher-degree Davenport constants over prime-power rings

Authors/Creators

Description

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.

Files

davenport_inverse_v1.pdf

Files (2.4 MB)

Name Size
md5:2daca0403b648fd7444b17f0cd2aad6a
309.7 kB Preview Download
md5:900a1fe013cca47f89454e259ddb1721
2.1 MB Preview Download