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- W2898210232 abstract "Let $p$ be an odd prime and let ${mathbb F}_p$ denote the finite field with $p$ elements. Suppose that $g$ is a primitive root of ${mathbb F}_p$. Define the permutation $tau_g:,{mathcal H}_pto{mathcal H}_p$ by $$ tau_g(b):=begin{cases} g^b,&text{if }g^bin{mathcal H}_p, -g^b,&text{if }g^bnotin{mathcal H}_p, end{cases} $$ for each $bin{mathcal H}_p$, where ${mathcal H}_p={1,2,ldots,(p-1)/2}$ is viewed as a subset of ${mathbb F}_p$. In this paper, we investigate the sign of $tau_g$. For example, if $pequiv 5pmod{8}$, then $$ (-1)^{|tau_g|}=(-1)^{frac{1}{4}(h(-4p)+2)} $$ for every primitive root $g$, where $h(-4p)$ is the class number of the imaginary quadratic field ${mathbb Q}(sqrt{-4p})$." @default.
- W2898210232 created "2018-11-02" @default.
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- W2898210232 date "2018-10-27" @default.
- W2898210232 modified "2023-09-27" @default.
- W2898210232 title "Some permutations over ${mathbb F}_p$ concerning primitive roots" @default.
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- W2898210232 hasPublicationYear "2018" @default.
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