2011/03/01 by Timothy S. Trudgian, Timothy Trudgian · 4 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Limits and Structures in Graph Theory
paper · pdf · doi:10.1090/s0025-5718-2011-02470-1
This article improves the estimate of the size of the definite integral of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S left-parenthesis t right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">S(t)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , the argument of the Riemann zeta-function. The primary application of this improvement is Turing’s Method for the Riemann zeta-function. Analogous improvements are given for the arguments of Dirichlet <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L"> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding="application/x-tex">L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -functions and of Dedekind zeta-functions.