On Kronecker limit formulas for real quadratic fields
| dc.creator | Yamamoto, Shuji | |
| dc.date | 2006-02-27 | |
| dc.date.accessioned | 2026-07-07T07:03:50Z | |
| dc.date.available | 2026-07-07T07:03:50Z | |
| dc.description | Let $ζ(s,C)$ be the partial zeta function attached to a ray class C of a real quadratic field. We study this zeta function at s=1 and s=0, combining some ideas and methods due to Zagier and Shintani. The main results are (1) a generalization of Zagier's formula for the constant term of the Laurent expansion at s=1, (2) some expressions for the value and the first derivative at s=0, related to the theory of continued fractions, and (3) a simple description of the behavior of Shintani's invariant X(C), which is related to $ζ'(0,C)$, when we change the signature of C. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602615 | |
| dc.identifier | http://arxiv.org/abs/math/0602615 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109129 | |
| dc.subject | Number Theory | |
| dc.subject | 11M20 | |
| dc.title | On Kronecker limit formulas for real quadratic fields | |
| dc.type | text |