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Low-lying zeros of L-functions for Quaternion Algebras
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The density conjecture of Katz and Sarnak predicts that, for natural families of L-functions, the distribution of zeros lying near the real axis is governed by a group of symmetry. In the case of the universal family of automorphic forms of bounded analytic conductor on a totally definite quaternion algebra, we determine the associated distribution for a restricted class of test functions. In particular it leads to non-trivial results on densities of non-vanishing at the central point.
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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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