Functional degrees and arithmetic applications III: Beyond Prime Exponent

2023/11/17 by Pete L. Clark, Clark, Pete L., Uwe Schauz +1
Mathematics · #13F20 #20C05 #20K01 #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2311.10527

openalex publication_date 2023/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Continuing our work on group-theoretic generalizations of the prime Ax-Katz Theorem, we give a lower bound on the p-adic divisibility of the cardinality of the set of simultaneous zeros Z(f₁,f₂,…,f_r) of r maps f_j:A→ B_j between arbitrary finite commutative groups A and B_j in terms of the invariant factors of A, B₁,B₂,\dotsc,B_r and the functional degrees of the maps f₁,f₂,\dotsc,f_r.

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