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Rational Points Near Curves and Small Nonzero |x3-y2| via Lattice Reduction
ANTS, pp.33-64, (2000)
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摘要
We give a new algorithm using linear approximation and lat- tice reduction to efficiently calculate all rational points of small height near a given plane curve C. For instance, when C is the Fermat cubic, we find all integer solutions of |x3 + y3 − z3| < M with 0 < x ≤ y < z < N in heuristic time ≪ (logO(1)N)M provided M ≫ N, using only ...更多
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