A Liouville-Type Inequality for Values of Mahler M-Functions

Key Points

• To establish a Liouville-type inequality for Mahler M-functions evaluated at a common algebraic point.
• Developed a theoretical framework for evaluating Mahler M-functions at a shared nonzero algebraic point.
• Analyzed the implications of the inequality within the context of number theory.
• Demonstrated that no evaluated value is a Liouville number.
• Confirmed that none of the values meet the criteria for being U-numbers.