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在半整数重量的实数零上,形成了赫克尖端
1Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland.
Mathematische annalen
|February 23, 2026
概括
这项研究研究了半整数重量赫克圆柱形态的零分布. 它表明,与模块化L函数相关的大量这些零点与靠近顶点的预测位置保持一致.
科学领域:
- 数学理论 数学理论
- 自体形的形式 自体形的形式
- 分析性的数理论.
背景情况:
- 赫克形是数论中的关键对象,它们的零分布揭示了深层次的算术性质.
- 戈什-萨尔纳克推测提出了古典的整体形赫克形状的零的特定位置.
- 了解这些零是推进分析数论中推测的关键.
研究的目的:
- 为了分析半整数重量的零的分布,赫克形状.
- 为了研究这些零点与特定垂直地理测量线的距离 (Re(s) = -1/2和Re(s) = 0).
- 为了将这些发现与古典形式的Ghosh-Sarnak猜测进行比较.
主要方法:
- 半整体重量的分析 赫克顶峰在
- 估计模块化L函数二次扭曲的平均第一和第二时刻.
- 随着重量K倾向于无限,对零分布的非对称分析.
主要成果:
- 显著数量的零值为半整体重量的Hecke尖端形状被证明是位于预测的垂直地测板上.
- 这些"真实"零的数量几乎以Ghosh-Sarnak猜测的类比所预测的速度增长.
- 对正比例的形式建立了一个较弱的实数零的下界.
结论:
- 这项研究提供了证据支持Ghosh-Sarnak猜测对半整体重量Hecke尖端形状的类比.
- 结果强调了模块化L函数及其扭曲在理解零分布方面的重要性.
- 这项工作有助于在数论中绘制零的分布的持续努力.
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