TY - JOUR
T1 - Functional degrees and arithmetic applications III
T2 - Beyond prime exponent
AU - Clark, Pete L.
AU - Schauz, Uwe
N1 - Publisher Copyright:
© The Author(s), 2025.
PY - 2025/5/30
Y1 - 2025/5/30
N2 - 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 $Z(f_1,f_2,\dotsc,f_r)$ 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 $f_1,f_2,\dotsc,f_r$.
AB - 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 $Z(f_1,f_2,\dotsc,f_r)$ 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 $f_1,f_2,\dotsc,f_r$.
UR - http://www.scopus.com/inward/record.url?scp=105007333928&partnerID=8YFLogxK
U2 - 10.1017/S0305004125000398
DO - 10.1017/S0305004125000398
M3 - Article
AN - SCOPUS:105007333928
SN - 0305-0041
SP - 1
EP - 30
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
ER -