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arXiv · 2311.10527

Functional degrees and arithmetic applications III: Beyond Prime Exponent

Pete L. Clark·Uwe Schauz
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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 $Z(f_1,f_2,\ldots,f_r)$ of $r$ maps $f_j:A\rightarrow B_j$ between arbitrary finite commutative groups $A$ and $B_j$ in terms of the invariant factors of $A, B_1,B_2,\dotsc,B_r$ and the \emph{functional degrees} of the maps $f_1,f_2,\dotsc,f_r$.

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Pete L. Clark, Uwe Schauz. 2023-11-17. Functional degrees and arithmetic applications III: Beyond Prime Exponent. https://doi.org/10.1017/s0305004125000398

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