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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.10527 |
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| _version_ | 1866908493633552384 |
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| author | Clark, Pete L. Schauz, Uwe |
| author_facet | Clark, Pete L. Schauz, Uwe |
| contents | 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 $f_1,f_2,\dotsc,f_r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10527 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Functional degrees and arithmetic applications III: Beyond Prime Exponent Clark, Pete L. Schauz, Uwe Number Theory Group Theory 20K01, 13F20, 20C05 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 $f_1,f_2,\dotsc,f_r$. |
| title | Functional degrees and arithmetic applications III: Beyond Prime Exponent |
| topic | Number Theory Group Theory 20K01, 13F20, 20C05 |
| url | https://arxiv.org/abs/2311.10527 |