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arXiv · 2301.06218

Fixed points of the sum of divisors function on $F_2[x]$

Luis H. Gallardo
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Abstract

We work an analogue of a classical arithmetic problem over polynomials. More precisely, we study the fixed points $F$ of the sum of divisors function $\sigma : F_2[x] \mapsto F_2[x]$ (defined \emph{mutatis mutandi} like the usual sum of divisors over the integers) of the form $F := A^2 \cdot S$, $S$ square-free, with $\omega(S) \leq 3$, coprime with $A$, for $A$ even, of whatever degree, under some conditions. This gives a characterization of $5$ of the $11$ known fixed points of $\sigma$ in $F_2[x]$

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Luis H. Gallardo. 2023-01-16. Fixed points of the sum of divisors function on $F_2[x]$. https://arxiv.org/abs/2301.06218

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