Related papers: Learning Euler Factors of Elliptic Curves
We consider elliptic transmission problems with complex coefficients across an interface. Under proper transmission conditions, that extend known conditions for well-posedness, and sub-ellipticity we derive microlocal and local Carleman…
Two-dimensional electronic spectroscopy has become one of the main experimental tools for analyzing the dynamics of excitonic energy transfer in large molecular complexes. Simplified theoretical models are usually employed to extract model…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…
Let $A$ be a $g$-dimensional abelian variety over $\mathbb{Q}$ whose adelic Galois representation has open image in $\text{GSp}_{2g} \widehat{\mathbb{Z}}$. We investigate the endomorphism algebras $\text{End}(A_p) \otimes \mathbb{Q} =…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
This study presents an innovative approach to predicting VCSEL emission characteristics using transformer neural networks. We demonstrate how to modify the transformer neural network for applications in physics. Our model achieved high…
Deep learning models can suffer from severe performance degradation when relying on spurious correlations between input features and labels, making the models perform well on training data but have poor prediction accuracy for minority…
Fix $p$ an odd prime. Let $E$ be an elliptic curve over $\mathbb{Q}$ with semistable reduction at $p$. We show that the adjoint $p$-adic $L$-function of $E$ evaluated at infinitely many integers prime to $p$ completely determines up to a…
We discuss several congruences satisfied by the coefficients of meromorphic modular forms, or equivalently, the $p$-adic behaviors of meromorphic modular forms under the $U_p$ operator, that are summarized from numerical experiments. In the…
Accurately estimating the refractive environment over multiple frequencies within the marine atmospheric boundary layer is crucial for the effective deployment of radar technologies. Traditional parabolic equation simulations, while…
The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We…
We present several new heuristic algorithms to compute class polynomials and modular polynomials modulo a prime $p$ by revisiting the idea of working with supersingular elliptic curves. The best known algorithms to this date are based on…
Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models…
Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of dimension two over finite fields. Although its correctness…
Can general-purpose AI architectures go beyond prediction to discover the physical laws governing the universe? True intelligence relies on "world models" -- causal abstractions that allow an agent to not only predict future states but…
We compute the Brauer group of the moduli stack of elliptic curves over the integers, localizations of the integers, finite fields of odd characteristic, and algebraically closed fields of characteristic not $2$. The methods involved…