Fixed Points of Maps on the Space of Rational Functions
Abstract
Given integers s,t, define a function phis,t on the space of all formal series expansions by phis,t (sum an xn) = sum asn+t xn. For each function phis,t, we determine the collection of all rational functions whose Taylor expansions at zero are fixed by phis,t. This collection can be described as a subspace of rational functions whose basis elements correspond to certain s-cyclotomic cosets associated with the pair (s,t).
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