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Estimates for denominators of Pade approximants and applications to Diophantine equations (13rit174)

The hypergeometric method of Thue and Siegel is a technique in Diophantine approximation that has proved to be widely applicable in number theory, ranging from classical results in Diophantine analysis (Thue and Thue–Mahler equations, unit equations) to much more analytic problems (gaps between k-free numbers). Despite being quite an old subject, the basic machinery underlying the approach (typically non-Archimedean valuations of off-diagonal Pade approximants) is not particularly well understood asymptotically.