Heegner's lemma
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Short description: Criterion for existence of polynomial roots
In mathematics, Heegner's lemma is a lemma used by Kurt Heegner in his paper on the class number problem. His lemma states that if
- [math]\displaystyle{ y^2=a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 }[/math]
is a curve over a field with a4 not a square, then it has a solution if it has a solution in an extension of odd degree.
References
- Birch, Bryan (2004), "Heegner points: the beginnings", in Darmon, Henri; Zhang, Shou-Wu, Heegner points and Rankin L-series, Math. Sci. Res. Inst. Publ., 49, Cambridge University Press, pp. 1–10, doi:10.1017/CBO9780511756375.002, ISBN 978-0-521-83659-3
![]() | Original source: https://en.wikipedia.org/wiki/Heegner's lemma.
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