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We present a new proof of the Manin-Mumford conjecture about torsion points on algebraic subvarieties of abelian varieties. Our principle, which admits other applications, is to view torsion points as rational points on a complex torus and then compare (i) upper bounds for the number of rational points on a transcendental analytic variety(More)
This paper presents an algorithm that, given an integer n > 1, finds the largest integer k such that n is a kth power. A previous algorithm by the first author took time b 1+o(1) where b = lg n; more precisely, time b exp(O(√ lg b lg lg b)); conjecturally, time b(lg b) O(1). The new algorithm takes time b(lg b) O(1). It relies on relatively complicated(More)
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