On the spectrum of irrationality exponents of Mahler numbers
On the spectrum of irrationality exponents of Mahler numbers
We consider Mahler functions f(z) which satisfy the functional equation f(z)=A(z) B(z)f(z d ) where A(z) B(z) is in ℚ(z) and d≥2 is an integer. We prove that, for any integer b with |b|≥2, either f(b) is rational or its irrationality exponent is rational. We also compute the exact value …