| Abstract: |
| Since the work of Montgomery and Odlyzko, there has been a significant body of literature on the similarities in the behavior of zeros of L-functions and the eigenvalues of random matrices. A major breakthrough came with the work of Katz and Sarnak, who demonstrated that while many random matrix ensembles share the same n-level correlations, there is another statistic, the n-level density, for which each ensemble has a different outcome. Moreover, most of the contribution to this statistic comes from the zeros near or at the central point, making it an ideal quantity for investigating the arithmetic of families. In this talk, we will discuss some new developments regarding the low-lying zeros of L-functions. |
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