The critical order of certain Hecke L-functions of imaginary quadratic fields

dc.creatorLiu, Chunlei
dc.creatorXu, Lanju
dc.date2002-10-21
dc.date.accessioned2026-07-07T04:52:10Z
dc.date.available2026-07-07T04:52:10Z
dc.descriptionLet $-D < -4$ 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.identifierhttps://arxiv.org/abs/math/0210313
dc.identifierhttp://arxiv.org/abs/math/0210313
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65368
dc.subjectNumber Theory
dc.subject11R42; 11G05
dc.titleThe critical order of certain Hecke L-functions of imaginary quadratic fields
dc.typetext

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