10 citations · 14 across the 10 of their papers we have counts for
11 papers
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 coefficients of the reduced minimal Weierstrass model of an elliptic curve are determined by the Diric…
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…
Jet fragmentation function and groomed substructure of bottom quark jets in proton-proton collisions at 5.02 TeV
CMS Collaboration
A measurement of the substructure of bottom quark jets (b jets) in proton-proton (pp) collisions is presented. The measurement uses data collected in pp collisions at =…
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…
Murmurations of Dirichlet characters
Kyu-Hwan Lee, Thomas Oliver, Alexey Pozdnyakov
We calculate murmuration densities for two families of Dirichlet characters. The first family contains complex Dirichlet characters normalized by their Gauss sums. Integrating the…
Fair pricing and hedging under small perturbations of the numéraire on a finite probability space
William Busching, Delphine Hintz, Oleksii Mostovyi +1
We consider the problem of fair pricing and hedging under small perturbations of the numéraire. We show that for replicable claims, the change of numéraire affects neither the fair…
Stochastic Scaling in Loss Functions for Physics-Informed Neural Networks
Ethan Mills, Alexey Pozdnyakov
Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult t…
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…