Titlebook: Algorithmic Number Theory; 4th International Sy Wieb Bosma Conference proceedings 2000 Springer-Verlag Berlin Heidelberg 2000 Algorithmic N

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Computing Special Values of Partial Zeta Functionscle for ..(ℤ); the special values are computed as periods of Ψ, and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.

Atheroma

On Reconstruction of Algebraic Numbers a number . if it exists such that . is smaller then the given bound and . ≡. mod ...The first application is an algorithm for the computation of .-th roots of algebraic numbers. Secondly, we get an algorithm to factor polynomials over number fields which generalizes the Hensel-factoring method. Our

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https://doi.org/10.1007/10722028Algorithmic Number Theory; Computational Number Theory; Elliptic Curve Computations; Factoring; Finite F

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Lice692

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Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensionsegrees of these extensions, which turns out to be the main difficulty. While in two special situations explicit formulas for the degrees are known, the general problem is solved algorithmically. The systematic application of the methods described yields several new examples of algebraic curves over . and . with comparatively many rational points.

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New Results on Lattice Basis Reduction in Practice lattice basis in practice. We analyze substantial experimental data and to our knowledge, we are the first to present a general heuristic for determining which variant of the reduction algorithm, for varied parameter choices, yields the most efficient reduction strategy for reducing a particular problem instance.