Timeline for Reference request: "A result of Siegel" related to Ramanujan-Nagell type equations
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2022 at 17:02 | comment | added | Eric Nathan Stucky | Thanks to everyone for the contributions :D | |
| Feb 13, 2022 at 16:24 | comment | added | Max Alekseyev | I've added the reference to Wikipedia: C. L. Siegel (1929). "Uber einige Anwendungen Diophantischer Approximationen". Abh. Preuss. Akad. Wiss. Phys. Math. Kl. 1: 41–69. | |
| Feb 13, 2022 at 7:37 | comment | added | Carlo Beenakker | an English translation of Siegel's 1929 paper is here | |
| Feb 13, 2022 at 7:05 | comment | added | alpoge | They’re referring to his $1929$ finiteness theorem for integral points, anyway it follows from Mordell’s finiteness theorem for integral points on $y^2 = x^3 + k$ [aka Mordell curves] cause you just split into cases based on what $n$ could be mod $3$ and you find three equations $x^2 + D = A\cdot (B^m)^3$, $x^2 + D = AB\cdot (B^m)^3$, and $x^2 + D = AB^2\cdot (B^m)^3$. Now just multiply through by $A^2$, $(AB)^2$, and $(AB^2)^2$ in each case and you’re reduced to finding integral points on a Mordell curve (Mordell proved there are finitely many such, Baker gave a way to actually find them). | |
| Feb 13, 2022 at 5:31 | history | asked | Eric Nathan Stucky | CC BY-SA 4.0 |