Functiones et Approximatio Commentarii Mathematici

Zero multiplicity and lower bound estimates of $|\zeta(s)|$

Anatolij Karatsuba

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Abstract

We give an improved lower bound for $\max_{|T-t|\leq H} |\zeta(\tfrac{1}{2} + it)|$ when $2 \leq \alpha H \leq \log\log T - c$, $1 \leq \alpha \lt \pi$. Our theorem slightly refines the result in [11]. We also prove a theorem about an upper bound for the multiplicities of zeros of $\zeta(s)$ conditionally, assuming some lower bound for $\max_{|s - s_1| \leq \Delta} |\zeta(s)|$.

Article information

Source
Funct. Approx. Comment. Math., Volume 35 (2006), 195-207.

Dates
First available in Project Euclid: 16 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229442623

Digital Object Identifier
doi:10.7169/facm/1229442623

Mathematical Reviews number (MathSciNet)
MR2271613

Zentralblatt MATH identifier
1196.11118

Subjects
Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 11N25: Distribution of integers with specified multiplicative constraints

Keywords
Riemann zeta-function zero multiplicity

Citation

Karatsuba, Anatolij. Zero multiplicity and lower bound estimates of $|\zeta(s)|$. Funct. Approx. Comment. Math. 35 (2006), 195--207. doi:10.7169/facm/1229442623. https://projecteuclid.org/euclid.facm/1229442623


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