Abstract
Given integers s, t, define a function φs,t on the space of all formal series expansions by φs,t( P anx ) = P asn+tx . For each function φs,t, we determine the collection of all rational functions whose Taylor expansions at zero are fixed by φs,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). Subject Class: Primary 33
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