论文标题
Dedekind Zeta功能的零密度
On density of the zeros of Dedekind zeta-functions
论文作者
论文摘要
对于任何$σ$，带有$ 0 \ leqσ\ leq 1 $和任何$ t> 10 $足够大的任何$n_ζ（σ，k，t）$是零$ρ=β+iγ$ $ quam $ζ_{k}（k}（s）$的零数量，并使用$ | c | c leq t $和$β\ geq \ geq q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q \ ex $ nive。对于$ k \ geq3，$我们有\ [n_ζ（σ，k，t）\ ll t^{\ frac {2k} {6σ-3} {6σ-3}（1-σ）+\ varepsilon}，\ \ \ \]，其中\ [\ frac {\ frac {2k+3} {2k+3} {2k+6} {2k+6} \ 1 <1 $ k $和$ \ varepsilon。$这改善了$σ$的某些范围的$ k \ geq3 $的先前结果。
For any $σ$ with $0\leq σ\leq 1$ and any $T>10$ sufficiently large, let $N_ζ(σ,K,T)$ be the number of zeros $ρ=β+iγ$ of $ζ_{K}(s)$ with $|γ|\leq T$ and $β\geq σ$ and the zero being counted according to multiplicity. For $k\geq3,$ we have \[ N_ζ(σ,K,T)\ll T^{\frac{2k}{6σ-3}(1-σ)+\varepsilon}, \] where \[ \frac{2k+3}{2k+6}\leq σ<1 \] and the implied constant may depend on the number field $K$ and $\varepsilon.$ This improves previous results for $k\geq3$ of certain range of $σ$.
