Andrew V. Sutherland

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math.NT2025

Decomposing a factorial into large factors

Boris Alexeev, Evan Conway, Matthieu Rosenfeld +4

Let $t (N)$ denote the largest number such that $N!$ can be expressed as the product of $N$ integers greater than or equal to $t (N)$ . The bound $t (N) / N = 1/ e - o (1)$ was apparently es…

math.NT2021

From the Birch and Swinnerton-Dyer conjecture to Nagao's conjecture

Seoyoung Kim, M. Ram Murty

Let $E$ be an elliptic curve over $Q$ with discriminant $Δ_{E}$ . For primes $p$ of good reduction, let $N_{p}$ be the number of points modulo $p$ and write $N_{p} = p + 1 - a_{p}$ . In 1…