17 citations · 75 across the 17 of their papers we have counts for
17 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…
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…
Machine Learning Class Numbers of Real Quadratic Fields
Malik Amir, Yang-Hui He, Kyu-Hwan Lee +2
We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separatin…
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…
Convergence of Kac--Moody Eisenstein Series over a function field
Kyu-Hwan Lee, Dongwen Liu, Thomas Oliver
We establish everywhere convergence in a natural domain for Eisenstein series on a symmetrizable Kac--Moody group over a function field. Our method is different from that of the af…
Machine-Learning Arithmetic Curves
Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver
We show that standard machine-learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around one hundred thousand, w…
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…
Twisting moduli for GL(2)
Benjamin Bedert, George Cooper, Thomas Oliver +1
We prove various converse theorems for automorphic forms on Γ_0(N), each assuming fewer twisted functional equations than the last. We show that no twisting at all is needed for ho…
Character expansion of Kac-Moody correction factors
Kyu-Hwan Lee, Dongwen Liu, Thomas Oliver
A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand the correction factor into a sum of irreducible characters of the underlyin…
Ratios of Artin L-functions
Leonhard Hochfilzer, Thomas Oliver
We show that certain quotients of Artin L-functions have infinitely many poles. Our result follows from a converse theorem for Maass forms of Laplace eigenvalue 1/4 in which the tw…
Weil's converse theorem for Maass forms and cancellation of zeros
Michael Neururer, Thomas Oliver
We prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that th…
A conjectural extension of Hecke's converse theorem
Sandro Bettin, Jonathan W. Bober, Andrew R. Booker +6
We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main…
Notes on Low Degree L-Data
Thomas Oliver
These notes are an extended version of a talk given by the author at the conference "Analytic Number Theory and Related Areas", held at Research Institute for Mathematical Sciences…
Zeta Functions on Arithmetic Surfaces
Thomas Oliver
We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this int…
Automorphicity and Mean-Periodicity
Thomas Oliver
If C is a smooth projective curve over a number field k, then, under fair hypotheses, its L-function admits meromorphic continuation and satisfies the anticipated functional equati…