Related papers: The complexity of elliptic normal bases

We evaluate the determinant of a matrix whose entries are elliptic hypergeometric terms and whose form is reminiscent of Sylvester matrices. A hypergeometric determinant evaluation of a matrix of this type has appeared in the context of…

The elliptic integral and its various generalizations are playing very important and basic role in different branches of modern mathematics. It is well known that they cannot be represented by the elementary transcendental functions.…

We prove that the extension complexity of the independence polytope of every regular matroid on $n$ elements is $O(n^6)$. Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a $O(n^2)$…

The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms-including Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) multiplication, as well as…

We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms…

We study the problem of counting lattice points of a polytope that are weighted by an Ehrhart quasi-polynomial of a family of parametric polytopes. As applications one can compute integrals and maximum values of such quasi-polynomials, as…

A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville Theorem for general phase transition potentials. Gradient estimates are…

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its…

There is a result related to the average number of the $(\delta, \eta)$-LLL bases in dimension $n$ in theoretical sense but the formula seems to be complicated and computing in high dimension takes a long time. In practical sense, we…

After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl(2m) that simplifies greatly the actual calculations and, without resorting to the conventional matrix…

In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete…

Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…

In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises…

We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in absence of regularity of solutions. To this end, we develop a substitute for…

In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to…

We study the elliptic modular surface attached to the commutator subgroup of the modular group. This has an elliptic curve as base and only one singular fibre. We employ an algebraic approach and then consider some arithmetic questions.

This paper studies three different ways to assign weights to the lattice points of a convex polytope and discusses the algebraic and combinatorial properties of the resulting weighted Ehrhart functions and their generating functions and…

In this paper, to the best of our knowledge, we make the first attempt at studying the parametric semilinear elliptic eigenvalue problems with the parametric coefficient and some power-type nonlinearities. The parametric coefficient is…

We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to…

We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing…