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Low-lying zeros of a large orthogonal family of automorphic $L$-functions
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abstract
We study a new orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q \asymp Q$. To illustrate our methods, we prove a one level density result for this family with the support of the Fourier transform of the test function being extended to be inside $(-4, 4)$. The main techniques developed in this paper will be useful in developing further results for this family, including estimates for high moments, information on the vertical distribution of zeros, as well as critical line theorems.
Forward citations
Cited by 2 Pith papers
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Low-lying zeros in families of Maass form L-functions: an extended density theorem
The Katz-Sarnak one-level density prediction for Maass form L-functions of prime level now holds for Fourier support up to 15/8, and up to 2 under the Grand Density Conjecture.
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Unitary $n$-correlations with restricted support in random matrix theory
The authors compute the Ratios-Theorem form of the U(N) n-correlation for Fourier support up to (-6,6), extending the q=1 and q=2 results of Conrey-Snaith and Chandee-Lee.
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