A new development of irrational number theory

点击翻译按钮获取中文摘要

For infinite product functions satisfying a chain of linear Mahler functional equations we established a useful sufficient condition for finiteness of the irrationality measure of the infinite product functions. We applied the condition to show a new criterion for algebraic independence of the values of the infinite product functions at the reciprocal of an integer. We also proved algebraic independence of the values of two infinite product functions at a general algebraic number by using elimination theory. Moreover, we investigate an axiomatic way of our method, which would have certain applications besides the infinite product functions.