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- W3129254192 abstract "Let $p$ be a prime, $m$ be a positive integer ( $m geq 1$, and $m geq 2$ if $p=2$), and $chi_n$ be a multiplicative complex character on $mathbb F^*_{p^m}$ with order $n| (p^m-1)$. We show that a partition $mathcal A_1 cup mathcal A_2 cup cdots cup mathcal A_n$ of $mathbb F^{*}_{p^m}$ is the partition by fibers of $chi_n$ if and only if these fibers %$mathcal A_i$ satisfy certain additive properties. This is equivalent to show that the set of multivariate characteristic polynomials of these fibers, completed with the constant polynomial $1$, is the basis of a $(n+1)$-dimensional commutative algebra with identity in the ring $mathbb Q[x_1,ldots,x_n]/langle x_1^p-1, ldots, x_n^p-1 rangle$." @default.
- W3129254192 created "2021-03-01" @default.
- W3129254192 creator A5080629927 @default.
- W3129254192 date "2021-02-15" @default.
- W3129254192 modified "2023-09-27" @default.
- W3129254192 title "On the Fiber Characters of $mathbb F^*_{p^m}$ and related Polynomial Algebras" @default.
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