Let $ \phi(z) = z^d + c $ be a polynomial over a field $ K. $ We study the inverse stability of $ \phi(z) $ over $ K. $ In this paper, we establish some sufficient conditions for the inverse stability of $ \phi(z) $ over the field of rational numbers and a function field. Furthermore, we also provide necessary and sufficient conditions for the inverse stability of $ \phi(z) $ over a finite field.
Citation: Yang Gao, Qingzhong Ji. On the inverse stability of $ z^n+c $[J]. Electronic Research Archive, 2025, 33(3): 1414-1428. doi: 10.3934/era.2025066
Let $ \phi(z) = z^d + c $ be a polynomial over a field $ K. $ We study the inverse stability of $ \phi(z) $ over $ K. $ In this paper, we establish some sufficient conditions for the inverse stability of $ \phi(z) $ over the field of rational numbers and a function field. Furthermore, we also provide necessary and sufficient conditions for the inverse stability of $ \phi(z) $ over a finite field.
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