Abstract
AbstractAssuming the generalized Riemann hypothesis, we provide explicit upper bounds for moduli of $$\log {\mathcal {L}(s)}$$
log
L
(
s
)
and $$\mathcal {L}'(s)/\mathcal {L}(s)$$
L
′
(
s
)
/
L
(
s
)
in the neighbourhood of the 1-line when $$\mathcal {L}(s)$$
L
(
s
)
are the Riemann, Dirichlet and Dedekind zeta-functions. To do this, we generalize Littlewood’s well-known conditional result to functions in the Selberg class with a polynomial Euler product, for which we also establish a suitable convexity estimate. As an application, we provide conditional and effective estimates for the Mertens function.
Publisher
Springer Science and Business Media LLC
Reference35 articles.
1. Backlund, R.J.: Über die Nullstellen der Riemannschen Zetafunktion. Acta Math. 41(1), 345–375 (1918)
2. Bourgain, J.: Decoupling, exponential sums and the Riemann zeta function. J. Am. Math. Soc. 30(1), 205–224 (2017)
3. Burckel, R.B.: Classical Analysis in the Complex Plane. Cornerstones, Birkhäuser/Springer, New York (2021)
4. Carneiro, E., Chandee, V.: Bounding $$\zeta (s)$$ in the critical strip. J. Number Theory 131(3), 363–384 (2011)
5. Chandee, V.: Explicit upper bounds for $$L$$-functions on the critical line. Proc. Am. Math. Soc. 137(12), 4049–4063 (2009)
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