Artin's Conjecture, Turing's Method, and the Riemann Hypothesis

@article{Booker2006ArtinsCT,
title={Artin's Conjecture, Turing's Method, and the Riemann Hypothesis},
author={Andrew R. Booker},
journal={Experimental Mathematics},
year={2006},
volume={15},
pages={385 - 407}
}
• A. Booker
• Published 25 July 2005
• Mathematics, Computer Science
• Experimental Mathematics
We present a group-theoretic criterion under which one may verify the Artin conjecture for some (nonmonomial) Galois representations, up to finite height in the complex plane. In particular, the criterion applies to S 5 and A 5 representations. Under more general conditions, the technique allows for the possibility of verifying the Riemann hypothesis for Dedekind zeta functions of nonabelian extensions of ℚ. In addition, we discuss two methods for locating zeros of arbitrary L-functions. The…

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