Roth's Theorem

For algebraic 👁 alpha

with 👁 epsilon>0
, has finitely many solutions. Klaus Roth received a Fields medal for this result.

See also

Hurwitz Equation, Hurwitz's Irrational Number Theorem, Irrationality Measure, Lagrange Number, Liouville's Approximation Theorem, Markov Number, Segre's Theorem, Siegel's Theorem

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References

Cassels, J. W. S. An Introduction to Diophantine Approximations. Cambridge, England: Cambridge University Press, 1957.Davenport, H. and Roth, K. F. "Rational Approximations to Algebraic Numbers." Mathematika 2, 160-167, 1955.Roth, K. F. "Rational Approximations to Algebraic Numbers." Mathematika 2, 1-20, 1955.Roth, K. F. "Corrigendum to 'Rational Approximations to Algebraic Numbers.' " Mathematika 2, 168, 1955.

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Roth's Theorem

Cite this as:

Weisstein, Eric W. "Roth's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RothsTheorem.html

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