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arXiv · 1604.03224

One-Level density for holomorphic cusp forms of arbitrary level

Owen Barrett·Paula Burkhardt·Jonathan DeWitt·Robert Dorward·Steven J. Miller
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Abstract

In 2000 Iwaniec, Luo, and Sarnak proved for certain families of $L$-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 Mili\'cevi\'c, which is of use for other problems as well.

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Owen Barrett, Paula Burkhardt, Jonathan DeWitt, Robert Dorward, Steven J. Miller. 2016-04-12. One-Level density for holomorphic cusp forms of arbitrary level. https://arxiv.org/abs/1604.03224

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