# Basic notions: Ehud de Shalit - The Loxton - van der Poorten conjecture

conjecture. It says the following. Let f be a Laurent power series (with complex

coefficients) and let \sigma_p be the operator substituting x^p for x in f. Suppose that f satisfies a homogenous polynomial equation in the operator \sigma_p with

coefficients which are rational functions, and a similar equation in the operator \sigma_q where p and q are multiplicatively independent natural numbers. Then f is a rational function.