7 papers · 1 filter
Murmurations of quadratic and cubic characters over function fields
Matilde Lalín, Kyu-Hwan Lee, Thomas Oliver +1
We compute the murmuration density for the family of quadratic characters over function fields. We show that the expectation of this density coincides with a correction term arisin…
Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves
Barinder S. Banwait, Xiaoyu Huang, Kyu-Hwan Lee +3
We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over may be computed from it's Frobenius traces. Decision tree mod…
On (not) learning the Möbius function
Alexey Pozdnyakov
We prove lower bounds on learning the Möbius or Liouville function with a variety of standard learning techniques, including kernel methods, noisy gradient methods, and correlation…
Murmurations: a case study in AI-assisted mathematics
Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver +1
We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmu…
Learning Euler Factors of Elliptic Curves
Angelica Babei, François Charton, Edgar Costa +5
We apply transformer models and feedforward neural networks to predict Frobenius traces from elliptic curves given other traces . We train further models to predict $a_p…
Predicting root numbers with neural networks
Alexey Pozdnyakov
We report on two machine learning experiments in search of statistical relationships between Dirichlet coefficients and root numbers or analytic ranks of certain low-degree -fun…