Titlebook: Algorithmic Number Theory; 7th International Sy Florian Hess,Sebastian Pauli,Michael Pohst Conference proceedings 2006 Springer-Verlag Berl

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https://doi.org/10.1007/978-3-8349-8700-6e present paper, the known lower bound 1.06 for . is raised to 1.218, and the known upper bound –1.009 for . is lowered to –1.229. In addition, the explicit upper bound of Pintz [14] on the smallest number for which the Mertens conjecture is false, is reduced from . to .. Finally, new numerical evid

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https://doi.org/10.1007/978-3-8349-8700-6nstein’s algorithm, which finds rigorous upper and lower bounds for Ψ(.,.). Bernstein’s original algorithm runs in time roughly linear in .. Our first, easy improvement runs in time roughly ... Then, assuming the Riemann Hypothesis, we show how to drastically improve this. In particular, if log. is

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https://doi.org/10.1007/978-3-662-06513-6han what was expected from the worst-case proved bounds, both in terms of the running time and the output quality. In this article, we investigate this puzzling statement by trying to model the average case of lattice reduction algorithms, starting with the celebrated Lenstra-Lenstra-Lovász algorith