The Sue and Gene Hotchkiss Celebration of Faculty Scholarship, 2017-2018

https://publications.lakeforest.edu/faculty_scholarship/1003/thumbnail.jp

Fixed points of the sum of divisors function on ({{mathbb{F}}}_2[x])

We work on an analogue of a classical arithmetic problem over polynomials. More precisely, we study the fixed points (F) of the sum of divisors function (sigma : {mathbb{F}}_2[x] mapsto {mathbb{F}}_2[x]) (defined 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 ({mathbb{F}}_2[x])