On explicit estimates for S(t), S1(t), and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>ζ</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn><mml:mo linebreak="badbreak" linebreakstyle="after">+</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mi>t</mml:mi><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:math> under the Riemann Hypothesis
نویسندگان
چکیده
Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $\zeta\left(1/2+\mathrm{i}t\right)$ while comparing them with recently proven unconditional ones. As a corollary obtain conditional bound on gaps between consecutive zeros zeta-function.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2022
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2021.05.014