339 citations · 6k across the 162 of their papers we have counts for
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Murmurations of elliptic curves
Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver +1
We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yiel…
Machine-Learning Number Fields
Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver
We show that standard machine-learning algorithms may be trained to predict certain invariants of algebraic number fields to high accuracy. A random-forest classifier that is train…
Machine-Learning the Sato--Tate Conjecture
Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver
We apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (betwee…
Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer
Laura Alessandretti, Andrea Baronchelli, Yang-Hui He
Empirical analysis is often the first step towards the birth of a conjecture. This is the case of the Birch-Swinnerton-Dyer (BSD) Conjecture describing the rational points on an el…
Cusps, Congruence Groups and Monstrous Dessins
Valdo Tatitscheff, Yang-Hui He, John McKay
We study general properties of the dessins d'enfants associated with the Hecke congruence subgroups of the modular group . The definition of th…