Related papers: Learning Euler Factors of Elliptic Curves

Artificial Neural Networks of varying architectures are generally paired with affine transformation at the core. However, we find dot product neurons with global influence less interpretable as compared to local influence of euclidean…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile…

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 yields a striking oscillating pattern, the details of which vary…

In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.

Characterizing the geometry of an object orbiting around a star from its transit light curve is a powerful tool to uncover various complex phenomena. This problem is inherently ill-posed, since similar or identical light curves can be…

Let $g \geq 1$ be an integer and let $A/\mathbb{Q}$ be an abelian variety that is isogenous over $\mathbb{Q}$ to %the product $E_1 \times \ldots \times E_g$ of elliptic curves $E_1/\mathbb{Q}$, $\ldots$, $E_g/\mathbb{Q}$, without complex…

We use the latest techniques in machine-learning to study whether from the landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones. Using the dataset of complete intersections in products of projective spaces (CICY3…

Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…

We propose a new model for counting $\mathbf{GL}_2(\mathbb{F}_p)$-number fields having the same local properties as the splitting field of the mod $p$-Galois representation associated with an elliptic curve over the rational numbers. We…

We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.

We obtain distribution results for traces of Frobenius for various families of elliptic curves with respect to the Lang-Trotter conjecture, extremal primes, and the central limit theorem. This includes some generalisations and bounds…

Let $E:y^2=x^3+ax+b$ be an elliptic curve defined over $\mathbb{Q}$. We compute certain twists of the classical modular curves $X(8)$. Searching for rational points on these twists enables us to find non-trivial pairs of $8$-congruent…

We developed a deep learning feed-forward network for estimating elliptic flow ($v_2$) coefficients in heavy-ion collisions from RHIC to LHC energies. The success of our model is mainly the estimation of $v_2$ from final state particle…

The well-known fact that all elliptic curves are modular, proven by Wiles, Taylor, Breuil, Conrad and Diamond, leaves open the question whether there exists a 'nice' representation of the modular form associated to each elliptic curve. Here…

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order…

Let $K$ be a fixed number field, assumed to be Galois over $\mathbb Q$. Let $r$ and $f$ be fixed integers with $f$ positive. Given an elliptic curve $E$, defined over $K$, we consider the problem of counting the number of degree $f$ prime…

Given an elliptic curve $E$ in Legendre form $y^2 = x(x - 1)(x - \lambda)$ over the fraction field of a Henselian ring $R$ of mixed characteristic $(0, 2)$, we present an algorithm for determining a semistable model of $E$ over $R$ which…

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…

We investigate a method to retrieve full-complex models (Transmission Matrix and Neural Network) of a highly multimode fiber (140 LP modes/polarization) using a straightforward machine learning approach, without the need of a reference…