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
Abstract
Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of S(t), S1(t), and ζ(1/2+it) while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional explicit bound on gaps between consecutive zeros of the Riemann...
Paper Details
Title
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
Published Date
Feb 1, 2022
Journal
Volume
231
Pages
464 - 491
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