Abstract.
Let be the approximation exponent of a power series α (so that when α is algebraic of degree d, then by Dirichlet’s and Liouville’s Theorems). If the characteristic is positive, q is a power of the characteristic, and are related by a fractional linear transformation with polynomial coefficients, then by respective work of Voloch and of de Mathan, there are constants such that has no solution if , and infinitely many solutions if . We will formulate and prove generalizations to simultaneous approximation.
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(Received 7 December 1999; in revised form 31 March 2000)
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Caulk, S., Schmidt, W. Simultaneous Approximation in Positive Characteristic. Mh Math 131, 15–28 (2000). https://doi.org/10.1007/s006050070021
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DOI: https://doi.org/10.1007/s006050070021