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Title:
Weighted statistics of the Riemann zeta function
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Abstract:
We will discuss classical statistics for the Riemann zeta function when the averages are tilted by powers of zeta on the critical line. In particular, we will focus on the weighted value-distribution of the Riemann zeta function, and statistics for its non-trivial zeros. This weighted investigation blends together the theory of moments and that of n-th level density, and allows for a better understanding of the interplay between zeros and large values of zeta.
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