Elliptic integral - Wikipedia
In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied
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Elliptic has been our trusted partner since 2015, helping strengthen our AML program and create a new standard for compliance in the crypto industry. We value their emphasis on data precision, as well as …
agens-no/EllipticCurveKeyPair
Sign, verify, encrypt and decrypt using the Secure Enclave (⭐ 726)
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Generalized Elliptic Integrals and Applications
We use some general properties, presented in previous work, to evaluate special cases of integrals relating Rogers-Ramanujan continued fraction, eta function and elliptic integrals....
Elliptic Curve Cryptography Explained
Points: 471 | Comments: 44 | Author: fangpenlin
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Elliptic has been our trusted partner since 2015, helping strengthen our AML program and create a new standard for compliance in the crypto industry. We value their emphasis on data precision, as well as …
Edwards curves and CM curves
Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic cur...
Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds
In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the...
Tamagawa numbers and positive rank of elliptic curves
This paper addresses the prediction of positive rank for elliptic curves without the need to find a point of infinite order or compute L-functions. While the most common method relies on parity conjectures, a recent technique introduced by Dokchitser...
Stripped elliptical galaxies as probes of ICM physics: I. Tails, wakes, and flow patterns…
Elliptical cluster galaxies are progressively stripped of their atmospheres due to their motion through the intra-cluster medium (ICM). Deep X-ray observations reveal the fine-structure of the galaxy's remnant atmosphere and its gas tail and wake. Th...
Fredholm Theory of Non-Elliptic Operators in the Presence of Normally Hyperbolic Trapping
We present an improved Fredholm theory of non-elliptic operators for when the corresponding classical dynamical system exhibits normally hyperbolic trapping with smooth backward and forward trapped sets. It takes place on coisotropic Sobolev spaces w...
The 2-parity conjecture for elliptic curves with isomorphic 2-torsion
The Birch and Swinnerton--Dyer conjecture famously predicts that the rank of an elliptic curve can be computed from its $L$-function. In this article we consider a weaker version of this conjecture called the parity conjecture and prove the following...
Gaussian Hypergeometric Evaluations of Traces of Frobenius for Elliptic Curves
We present here a formula for expressing the trace of the Frobenius endomorphism of an elliptic curve $E$ over $\mathbb{F}_q$ satisfying $j(E)\neq 0,1728$ and $q\equiv 1 \pmod{12}$ in terms of special values of Gaussian hypergeometric series. This...
A robust solver for elliptic PDEs in 3D complex geometries
We develop a boundary integral equation solver for elliptic partial differential equations on complex \threed geometries. Our method is efficient, high-order accurate and robustly handles complex geometries. A key component is our singular and near-s...
A note on integral points on elliptic curves
We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficients, we are led to suspect four extremal cases that still might have...
Torsion primes for elliptic curves over degree 8 number fields
Let $d\geq 1$ be an integer and let $p$ be a rational prime. Recall that $p$ is a torsion prime of degree $d$ if there exists an elliptic curve $E$ over a degree $d$ number field $K$ such that $E$ has a $K$-rational point of order $p$. Derickx, Kamie...
A general existence proof for non-linear elliptic equations in semi-Riemannian spaces
We present a general existence proof for a wide class of non-linear elliptic equations which can be applied to problems with barrier conditions without specifying any assumptions guaranteeing the uniqueness or local uniqueness of particular solutio...
Graviton Production in Elliptical and Hyperbolic Universes
The problem of cosmological graviton creation for homogeneous and isotropic universes with elliptical ($\vae =+1$) and hyperbolical ($\vae =-1$) geometries is addressed. The gravitational wave equation is established for a self-gravitating fluid sa...