Alexander Smith

activity

20132026

most citedAbelian varieties of prescribed order over finite fields

4 citations · 4 across the 5 of their papers we have counts for

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math.NT2025

Lattice points in thickened parabolas and rational points near hypersurfaces

Alexander Smith

Among the nondegenerate C^4 hypersurfaces M in R^n, we characterize the rational quadrics as the hypersurfaces that are the least well approximated by rational points. Given M othe…

math.NT2025

The Birch and Swinnerton-Dyer conjecture implies Goldfeld's conjecture

Alexander Smith

Given an elliptic curve E/Q, we show that 50% of the quadratic twists of E have $2^{\infty}$ -Selmer corank 0 and 50% have $2^{\infty}$ -Selmer corank 1. As one consequence, we prove…