21 citations · 125 across the 34 of their papers we have counts for
38 papers
Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves
Joanna Bieri, Edgar Costa, Alyson Deines +5
We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over and evaluate and interpret their predictive capacity. In keeping…
On Murmurations and Trace Formulas
David Lowry-Duda
In recent work with Bober, Booker, Lee, Seymour-Howell, and Zubrilina, we proved murmuration behavior for Maass forms in the eigenvalue aspect and for modular forms in the weight a…
Machine learning the vanishing order of rational L-functions
Joanna Bieri, Giorgi Butbaia, Edgar Costa +6
In this paper, we study the vanishing order of rational -functions from a data scientific perspective. Each -function is represented in our data by finitely many Dirichlet co…
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…
A database of rigorous Maass forms
David Lowry-Duda
We announce a database of rigorously computed Maass forms on congruence subgroups and briefly describe the methods of computation.
The Fibonacci Zeta Function and Modular Forms
Eran Assaf, Chan Ieong Kuan, David Lowry-Duda +1
We show that a family of Dirichlet series generalizing the Fibonacci zeta function has meromorphic continuation in terms of dihedral Maass forms.
Studying number theory with deep learning: a case study with the Möbius and squarefree indicator functions
David Lowry-Duda
Building on work of Charton, we train small transformer models to calculate the Möbius function and the squarefree indicator function . The models attain nontrivial…
Learning Fricke signs from Maass form Coefficients
Joanna Bieri, Giorgi Butbaia, Edgar Costa +6
In this paper, we conduct a data-scientific investigation of Maass forms. We find that averaging the Fourier coefficients of Maass forms with the same Fricke sign reveals patterns…
The Fibonacci Zeta Function and Continuation
Eran Assaf, Chan Ieong Kuan, David Lowry-Duda +1
We introduce a family of Dirichlet series associated to real quadratic number fields that generalize the ordinary Fibonacci zeta function , where denotes the…
Murmurations of Maass forms
Andrew R. Booker, Min Lee, David Lowry-Duda +2
We prove the existence of murmurations in the family of Maass forms of weight 0 and level 1 with their Laplace eigenvalue parameter going to infinity (i.e., correlations between th…
Towards a classification of isolated -invariants
Abbey Bourdon, Sachi Hashimoto, Timo Keller +5
We develop an algorithm to test whether a non-CM elliptic curve gives rise to an isolated point of any degree on any modular curve of the form . This builds…
Counting Divisors in the Outputs of a Binary Quadratic Form
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1
For a fixed natural number , we prove meromorphic continuation of the two-variable Dirichlet series to and use this to…
Murmurations of modular forms in the weight aspect
Jonathan Bober, Andrew R. Booker, Min Lee +1
We prove the existence of "murmurations" in the family of holomorphic modular forms of level and weight , that is, correlations between their root numbers and Hecke…
Sums of Cusp Form Coefficients Along Quadratic Sequences
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1
Let be a cusp form of weight on with character . By studying a certain shifted convolution sum, we prove that $\sum_{n \…
Improved bounds on number fields of small degree
Theresa C. Anderson, Ayla Gafni, Kevin Hughes +5
We study the number of degree number fields with discriminant bounded by . In this article, we improve an upper bound due to Schmidt on the number of such fields that was pr…
Prime Sums
Anupam Datta, Nir Elber, Raymond Feng +2
We study the properties of certain graphs involving the sums of primes. Their structure largely turns out to relate to the distribution of prime gaps and can be roughly seen in Cra…
Sign changes of cusp form coefficients on indices that are sums of two squares
David Lowry-Duda
We study sign changes in the sequence , where are the coefficients of a holomorphic cuspidal Hecke eigenform. After proving a variant of an axiom…
Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver +3
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert…
Towards Flying through Modular Forms
David Lowry-Duda, Adam Sakareassen
Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing wor…
Arithmetic Progressions of Squares and Multiple Dirichlet Series
Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1
We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic conti…
Visualizing modular forms
David Lowry-Duda
We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of e…
Computing classical modular forms
Alex J. Best, Jonathan Bober, Andrew R. Booker +8
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
Congruent number triangles with the same hypotenuse
David Lowry-Duda, Brendan Hassett
In this article, we discuss whether a single congruent number can have two (or more) distinct triangles with the same hypotenuse. We also describe and carry out computational e…
Non-real Poles and Irregularity of Distribution
David Lowry-Duda
We study the general theory of weighted Dirichlet series and associated summatory functions of their coefficients. We show that any non-real pole leads to oscillatory error terms.…