TOPICS
Search

Roth's Theorem

For algebraic alpha

|alpha-p/q|<1/(q^(2+epsilon)),

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

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Roth's Theorem

Cite this as:

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

Subject classifications