Timeline for Sign of the special value at s=0 of Hecke L-functions
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2022 at 20:42 | comment | added | François Brunault | In general, these signs (or arguments) will be controlled by the root numbers of the $L$-function, which are analogue to Gauss sums and can be quite difficult to determine (one may think of the problem of determining the sign of the classical quadratic Gauss sum). | |
| Jan 21, 2022 at 12:17 | vote | accept | Adrien MORIN | ||
| Jan 21, 2022 at 12:17 | answer | added | Adrien MORIN | timeline score: 2 | |
| Jan 21, 2022 at 12:04 | answer | added | David Loeffler | timeline score: 4 | |
| Jan 21, 2022 at 12:02 | history | edited | Adrien MORIN | CC BY-SA 4.0 |
corrected a typo, restricted the question to real characters
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| Jan 21, 2022 at 11:26 | comment | added | Adrien MORIN | @DavidLoeffler I was looking at Artin L-functions of rational representations initially, and wanted to reduce to Hecke L-functions by Artin induction. But I overlooked that the special value is then not necessarily a real number indeed. | |
| Jan 21, 2022 at 11:24 | comment | added | Adrien MORIN | @DavidFarmer It is -1 for the trivial character, I have edited my post. | |
| Jan 20, 2022 at 15:23 | comment | added | KConrad | Are you asking for the factor of absolute value 1 in its polar decomposition? Unless $\chi$ is real-valued, that factor is unlikely to be $\pm 1$. | |
| Jan 20, 2022 at 15:20 | comment | added | David Farmer | Is your conjecture 1 for trivial character or -1 for trivial character? | |
| Jan 20, 2022 at 14:55 | comment | added | David Loeffler | Why should it be a real number? | |
| Jan 20, 2022 at 14:36 | history | asked | Adrien MORIN | CC BY-SA 4.0 |