On multiplicative independence of rational function iterates
On multiplicative independence of rational function iterates
Abstract We give lower bounds for the degree of multiplicative combinations of iterates of rational functions (with certain exceptions) over a general field, establishing the multiplicative independence of said iterates. This leads to a generalisation of Gao’s method for constructing elements in the finite field $${\mathbb {F}}_{q^n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi><mml:msup><mml:mi>q</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:msub></mml:math> whose …