Algebra/Number Theory Seminar
The \(a\)-values of the Riemann zeta function near the critical line
Yoonbook Lee, Incheon National U
12:00 PM - 1:00 PM
Hylan 1106A
We study the value distribution of the Riemann zeta function near the line \(\Re s = 1/2\). We find an asymptotic formula for the number of \(a\)-values in the rectangle \(1/2 + h_1 / (\log T)^\theta \leq \Re s \leq 1/2+ h_2 /(\log T)^\theta\), \(T \leq \Im s \leq 2T\) for fixed \(h_1, h_2>0\) and \(0 < \theta <1/13\). To prove it, we need an extension of the valid range of Lamzouri, Lester and Radziwill’s recent results on the discrepancy between the distribution of \(\zeta(s)\) and its random model. We also propose the secondary main term for the Selberg’s central limit theorem by providing sharper estimates on the line \(\Re s = 1/2 + 1/(\log T)^\theta\). This is a joint work with Junsoo Ha in KIAS.
Event contact: dinesh dot thakur at rochester dot edu
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