Timeline for Verifying coefficients of modular forms
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2011 at 5:57 | comment | added | JSE | Right, that was the case in the applications I seem to remember (though of course so many more Galois representations are provably modular these days...) | |
| Feb 8, 2011 at 15:20 | comment | added | François Brunault | @JSE : in the situation you describe, isn't the method even perfectly rigourous (because Fourier coefficients are integers, it suffices to find approximate them within $1/2$). Ah, maybe the problem is that in general the functional equation of the L-function is only conjectural ? | |
| Feb 8, 2011 at 14:36 | comment | added | JSE | This "approximate functional equation" technique is surprisingly useful in practice. For instance: sometimes you have the L-function of a variety at all primes except, say, 2, because the special fiber at 2 is horrible. But the method described here allows you to guess the Euler factor at 2 with moral certainty if you know (a long list of) the other Euler factors. | |
| Feb 8, 2011 at 12:04 | history | answered | François Brunault | CC BY-SA 2.5 |