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Creators/Authors contains: "Erukulangara, Muhammed Rashad"

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  1. ; (, Advances in Mathematics of Communications)
    We present a proof under a generalization of the Riemann Hypothesis that the class group algorithm of Hafner and McCurley runs in expected time \begin{document}$$ e^{\left(3/\sqrt{8}+o(1)\right)\sqrt{\log d\log\log d}} $$\end{document} where \begin{document}$ -d $$\end{document} is the discriminant of the input imaginary quadratic order. In the original paper, an expected run time of \begin{document}$$ e^{\left(\sqrt{2}+o(1)\right)\sqrt{\log d\log\log d}} $$\end{document}$ was proven, and better bounds were conjectured. To achieve a proven result, we rely on a mild modification of the original algorithm, and on recent results on the properties of the Cayley graph of the ideal class group. 
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