Improvements to Turing’s method-Reference-Cited by-同舟云学术

Improvements to Turing’s method

Published:2011-03-01 Issue:276 Volume:80 Page:2259-2279
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Trudgian Timothy

Abstract

This article improves the estimate of the size of the definite integral of S ( t ) S(t) , 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 L L -functions and of Dedekind zeta-functions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2011-80-276/S0025-5718-2011-02470-1/S0025-5718-2011-02470-1.pdf

Reference21 articles.

1. R. J. Backlund. Sur les zéros de la fonction 𝜁(𝑠) de Riemann. Comptes rendus de l’Académie des sciences, 158:1979–1982, 1914.

2. Artin’s conjecture, Turing’s method, and the Riemann hypothesis;Booker, Andrew R.;Experiment. Math.,2006

3. On the zeros of the Riemann zeta function in the critical strip;Brent, Richard P.;Math. Comp.,1979

4. Graduate Texts in Mathematics;Davenport, Harold,1980

5. Pure and Applied Mathematics, Vol. 58;Edwards, H. M.,1974

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