Timeline for Consequences of infinitely many double zeros of zeta function of number field
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2021 at 16:48 | comment | added | joro | @KConrad In your example with $n^2$ I have the properties "never prime" and "always squareful", which would be an answer to the question. | |
| Sep 23, 2021 at 0:24 | comment | added | KConrad | Those double zeros are artificial, because they are coming from an $L$-function that appears inside the zeta-function of $K$ with multiplicity greater than $1$. It's sort of like asking if the repeated prime factors in a perfect square $n^2$ for $n > 1$ could imply some property of prime numbers. What is interesting are higher-order (meaning not of order $1$) nontrivial zeros for an $L$-function that does not (or is at least not expected to) decompose into other $L$-functions; such phenomena do happen in the setting of the Birch and Swinnerton-Dyer conjecture. | |
| Sep 22, 2021 at 21:48 | answer | added | 2734364041 | timeline score: 5 | |
| Sep 22, 2021 at 15:26 | comment | added | user334725 | For Q2, usually one considers primitive $L$-functions, and the only Dedekind $\zeta$-function that is primitive is that for the rationals. So the fact that $\zeta_K$ for general $K$ can have higher order zeros (due to primitive factors occurring with high multiplicity) is not so relevant. | |
| Sep 22, 2021 at 15:13 | history | asked | joro | CC BY-SA 4.0 |