Linear independence measures for infinite products

Abstract

Let f be an entire transcendental function with rational coefficients in its power series about the origin. Further, let f satisfy a functional equationand some particular c ∈ Q. Then the linear independence of 1, f (α), f (−α) over Q for non-zero α ∈ Q is proved, and a linear independence measure for these numbers is given. Clearly, for Q = 0 the function f can be written as an infinite product.