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- W1982200828 abstract "Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions towards a Gaussian field, with covariance structure corresponding to the $HH^{1/2}$-norm of the test functions. For this purpose, we obtain an approximate form of the explicit formula, relying on Selberg's smoothed expression for $zeta'/zeta$ and the Helffer-Sjostrand functional calculus. Our main result is an analogue of the strong Szeg{H o} theorem, known for Toeplitz operators and random matrix theory." @default.
- W1982200828 created "2016-06-24" @default.
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- W1982200828 date "2012-03-23" @default.
- W1982200828 modified "2023-09-23" @default.
- W1982200828 title "Strong Szego asymptotics and zeros of the zeta function" @default.
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- W1982200828 doi "https://doi.org/10.48550/arxiv.1203.5328" @default.
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