On Shintani's ray class invariant for totally real number fields
| dc.creator | Yamamoto, Shuji | |
| dc.date | 2008-05-28 | |
| dc.date.accessioned | 2026-07-07T09:41:18Z | |
| dc.date.available | 2026-07-07T09:41:18Z | |
| dc.description | We introduce a ray class invariant $X(C)$ for a totally real field, following Shintani's work in the real quadratic case. We prove a factorization formula $X=X_1... X_n$ where each $X_i=X_i(C)$ corresponds to a real place. Although this factorization depends a priori on some choices (especially on a cone decomposition), we can show that it is actually independent of these choices. Finally, we describe the behavior of $X_i(C)$ when the signature of $C$ at a real place is changed. This last result is also interpreted into an interesting behavior of the derivative $L'(0,χ)$ of $L$-functions. | |
| dc.description | 28 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0805.4282 | |
| dc.identifier | http://arxiv.org/abs/0805.4282 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161784 | |
| dc.subject | Number Theory | |
| dc.subject | 11M20 (Primary) 11R42, 11R80 (Secondary) | |
| dc.title | On Shintani's ray class invariant for totally real number fields | |
| dc.type | text |