A product formula of Mumford forms, and the rationality of Ruelle zeta values for Schottky groups

In any positive genus case, we show an explicit formula of the Mumford forms expressed by infinite products like Selberg type zeta values for Schottky groups. This result is considered as an extension of the formula in terms of Ramanujan’s Delta function in the genus 1 case, and is especially applied to studying the rationality of Ruelle zeta values for Schottky groups.