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20132022
most citedModeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves

36 citations · 90 across the 10 of their papers we have counts for

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Showing 2015 · math.ACShow all

3 papers · 2 filters

math.AC2015★ 3 cited

Algorithms for commutative algebras over the rational numbers

H. W. Lenstra, A. Silverberg

The algebras considered in this paper are commutative rings of which the additive group is a finite-dimensional vector space over the field of rational numbers. We present determin…

math.AC2015★ 8 cited

Roots of unity in orders

H. W. Lenstra, A. Silverberg

We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the or…

math.AC2015

Determining cyclicity of finite modules

H. W. Lenstra, A. Silverberg

We present a deterministic polynomial-time algorithm that determines whether a finite module over a finite commutative ring is cyclic, and if it is, outputs a generator.