Timeline for Striking applications of Baker's theorem
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2010 at 17:38 | comment | added | Micah Milinovich | I agree with Gerry. The last sentence of Stark's states: "Gelfond and Linnik's idea coupled with Gelfond's effective theorem on linear forms in two logarithms would have settled the class-number one problem in 1949 had only the expansion in (2) been available with characters to nonprime moduli." But this expansion was not available, it was proved by Stark in the 1960s. | |
| Jul 29, 2010 at 6:14 | comment | added | Gerry Myerson | @Junkie, my reading of the Stark paper is that one also needs a result on L-functions that was only published (by Stark) in 1968/69. But perhaps this result, too, could have been proved by Gelfond and Linnik in 1949. Anyway, thanks for the pointer to Stark's paper. | |
| Jul 28, 2010 at 12:31 | comment | added | Anweshi | @Junkie. Thanks. I didn't know that it could be obtained using merely Gelfond-Schneider. But it seems the case that Baker's theorem got its fame firstly through this achievement, if I am not mistaken. | |
| Jul 28, 2010 at 12:29 | comment | added | Junkie | Except that it was unneeded there, as pointed out in the aftermath by Stark. You only needed two logs, and then its just Gelfond (and effective) which is much simpler. Similar to other historical cases, what is the bottleneck is not always the first to seem to be the crux in retrospect. ams.org/journals/proc/1969-021-01/S0002-9939-1969-0237461-X/… | |
| Jul 28, 2010 at 11:11 | comment | added | Anweshi | Oh, yes! I had forgotten it as my mind was full of the work of Heegner, Dorian Goldfeld, etc! Surely, it is the most striking. | |
| Jul 28, 2010 at 1:55 | history | answered | Gerry Myerson | CC BY-SA 2.5 |