Timeline for What are the unsolved problems in Formal groups and $L$-functions?
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8 events
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| Sep 26, 2023 at 17:37 | comment | added | MAS | @DavidLoeffler, thank you for pointing out the paper of Kobayashi. I hope it will guide me | |
| Sep 26, 2023 at 17:32 | comment | added | MAS | @DavidLoeffler, thanks. Regarding your 2nd comment, my question is that Honda considered the L-function with dirichlet-character defined by discriminant $d$ of quadratic extension of $\mathbb Q$ and he proved that the associated formal group is $F(x,y)=x+y+\sqrt{d} xy$. My question, if I consider a dirichlet L-function involving other characters in some finite extensions (e.g., cubic or cyclotomic) of $\mathbb Q$, then we might get a different a formal group law. Is it good question in your opinion? | |
| Sep 26, 2023 at 15:01 | comment | added | David Loeffler | Regarding other (rather different) kinds of links between formal groups and values of L-functions, you might enjoy e.g. this paper of Kobayashi from a few years back: S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. math. 152 (2003) 1, 1-36. | |
| Sep 26, 2023 at 14:59 | comment | added | David Loeffler | It's a rather "fragile" statement which doesn't generalise well (e.g. for an elliptic curve over a number field $F \ne \mathbb{Q}$ there is no statement like this). | |
| Sep 26, 2023 at 14:56 | comment | added | David Loeffler | The relation between the formal-group logarithm and the L-series, for an elliptic curve over the rationals, is discussed here: mathoverflow.net/questions/52241/formal-group-laws-and-l-series | |
| Sep 26, 2023 at 14:23 | history | edited | MAS | CC BY-SA 4.0 |
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| Sep 26, 2023 at 11:12 | history | edited | MAS | CC BY-SA 4.0 |
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| Sep 26, 2023 at 5:44 | history | asked | MAS | CC BY-SA 4.0 |