论文标题
离散的平均估计和Landau-Siegel Zero
Discrete mean estimates and the Landau-Siegel zero
论文作者
论文摘要
令$χ$为模量$ d $的真正原始字符。证明$$ l（1，χ）\ gg（\ log d）^{ - 2022} $$，其中隐含常数是绝对且有效地计算的。 在证明中，$ l（1，χ）$的下限首先与某个地区的Dirichlet $ l $ functions的零分布有关，并且得出了连续零之间的差距的一些结果。然后，通过评估大筛型的某些离散手段，如果$ l（1，χ）$太小，可以获得矛盾。
Let $χ$ be a real primitive character to the modulus $D$. It is proved that $$ L(1,χ)\gg (\log D)^{-2022} $$ where the implied constant is absolute and effectively computable. In the proof, the lower bound for $L(1,χ)$ is first related to the distribution of zeros of a family of Dirichlet $L$-functions in a certain region, and some results on the gaps between consecutive zeros are derived. Then, by evaluating certain discrete means of the large sieve type, a contradiction can be obtained if $L(1,χ)$ is too small.
