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Seminar
FIELD Mathematics
DATE October 14 (Thu), 2021
TIME 16:00-17:00
PLACE Online
SPEAKER Lee, Yoonbok
HOST Choi, Junhwa
INSTITUTE 인천대학교
TITLE [GS_M_NT] The a-values of the Riemann zeta function near the critical line
ABSTRACT

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 / (logT)^\theta \leq Re(s) \leq 1/2 + h_2 / (logT)^\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 Radziwiłł’s recent results on the discrepancy between the distribution of the Riemann zeta function 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/(logT)^\theta$.

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