Linear independence measures for infinite products
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Let f be an entire transcendental function with rational coefficients in its power series about the origin. Further, let f satisfy a functional equation f(qz)= (z−c)f(z)+Q(z) with \(\) and 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.
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