Low-lying zeros of number field L-functions
Low-lying zeros of number field L-functions
复制标题
数域 L 函数的低位零点
DOI：
10.1016/j.jnt.2012.05.034
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发表时间：
2010
影响因子：
0.7
通讯作者：
Ryan Peckner
中科院分区：
文献类型：
--
作者：
Steven J. Miller;Ryan Peckner
在研究l函数的零点时，最重要的统计数据之一是1级密度，它测量零点在中心点附近的浓度。Fouvry和Iwaniec (2003) [FI]证明了虚二次域上l函数的1能级密度与随机矩阵理论预测的结果一致。在本文中，我们证明了在更一般的数域序列中出现的与随机矩阵理论相似的一致性。我们首先证明主项符合随机矩阵理论，并且与迄今为止研究的所有其他族相似，与场的算术无关。然后，我们推导出1级密度的第一个低阶项，并看到算术进入。视频：观看本文的视频摘要，请点击这里或访问http://www.youtube.com/watch?v=zpb-gu3G8i0。
TEXT: One of the most important statistics in studying the zeros of L-functions is the 1-level density, which measures the concentration of zeros near the central point. Fouvry and Iwaniec (2003) [FI] proved that the 1-level density for L-functions attached to imaginary quadratic fields agrees with results predicted by random matrix theory. In this paper, we show a similar agreement with random matrix theory occurring in more general sequences of number fields. We first show that the main term agrees with random matrix theory, and similar to all other families studied to date, is independent of the arithmetic of the fields. We then derive the first lower order term of the 1-level density, and see the arithmetic enter. VIDEO: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=zpb-gu3G8i0.