\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Multiplicative independence}{}% 2
\BOOKMARK [1][-]{section.3}{An arithmetic implicit function theorem}{}% 3
\BOOKMARK [1][-]{section.4}{Concluding remarks}{}% 4
\BOOKMARK [1][-]{section.5}{Acknowledgment}{}% 5