Siegel's Theorem

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates.

The second states that if 👁 xi
is an algebraic number of degree 👁 r
, then there is an 👁 A(xi)
depending only on 👁 xi
such that

for all integer 👁 p
and 👁 q
(Landau 1970, pp. 37-56; Hardy 1999, p. 79).

See also

Elliptic Curve, Roth's Theorem

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References

Davenport, H. "Siegel's Theorem." Ch. 21 in Multiplicative Number Theory, 2nd ed. New York: Springer-Verlag, pp. 126-125, 1980.Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.Landau, E. Vorlesungen über Zahlentheorie, Vol. 3. New York: Chelsea, 1970.

Referenced on Wolfram|Alpha

Siegel's Theorem

Cite this as:

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

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