One-level density for holomorphic cusp forms of arbitrary level
One-level density for holomorphic cusp forms of arbitrary level
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DOI：
10.1007/s40993-017-0091-9
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发表时间：
2016-04
影响因子：
0.8
通讯作者：
Owen Barrett;Paul Burkhardt;Jonathan DeWitt;R. Dorward;Steven J. Miller
中科院分区：
文献类型：
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作者：
Owen Barrett;Paul Burkhardt;Jonathan DeWitt;R. Dorward;Steven J. Miller
2000 年，Iwaniec、Luo 和 Sarnak 证明了与无平方能级的全纯新形式相关的某些 L 函数族，在广义黎曼假设下，当导体趋于无穷大时，其零点的单能级密度与来自某些经典紧群的大型随机矩阵在适当的标度极限下的特征值的单能级密度相匹配。我们通过使用 Blomer 和 Milićević 开发的基础获得任意级别的迹公式来消除无平方限制，该公式也可用于其他问题。
In 2000 Iwaniec, Luo, and Sarnak proved for certain families ofL-functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis, as the conductors tend to infinity the one-level density of their zeros matches the one-level density of eigenvalues of large random matrices from certain classical compact groups in the appropriate scaling limit. We remove the square-free restriction by obtaining a trace formula for arbitrary level by using a basis developed by Blomer and Milićević, which is of use for other problems as well.