The critical order of certain Hecke L-functions of imaginary quadratic fields
| dc.creator | Liu, Chunlei | |
| dc.creator | Xu, Lanju | |
| dc.date | 2002-10-21 | |
| dc.date.accessioned | 2026-07-07T04:52:10Z | |
| dc.date.available | 2026-07-07T04:52:10Z | |
| dc.description | Let $-D < -4$ denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of $\Bbb Q(\sqrt{-D})$ exists. Let $d$ be a fundamental discriminant prime to $D$. Let $2k-1$ be an odd natural integer prime to the class number of $\Bbb Q(\sqrt{-D})$. Let $χ$ be the twist of the $(2k-1)$th power of a canonical Hecke character of $\Bbb Q(\sqrt{-D})$ by the Kronecker's symbol $n\mapsto(\frac{d}{n})$. It is proved that the order of the Hecke $L$-function $L(s,χ)$ at its central point $s=k$ is determined by its root number when $|d| \leq c(ε)D^{{1/24}-ε}$ or, when $|d| \leq c(ε)D^{\frac1{12} -ε}$ and $k\geq 2$, where $ε> 0$ and $c(ε)$ is a constant depending only on $ε$. | |
| dc.identifier | https://arxiv.org/abs/math/0210313 | |
| dc.identifier | http://arxiv.org/abs/math/0210313 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65368 | |
| dc.subject | Number Theory | |
| dc.subject | 11R42; 11G05 | |
| dc.title | The critical order of certain Hecke L-functions of imaginary quadratic fields | |
| dc.type | text |