Related papers: The Signs in Elliptic Nets
We study Severi curves parametrizing rational bisections of elliptic fibrations associated to general pencils of plane cubics. Our main results show that these Severi curves are connected and reduced, and we give an upper bound on their…
We extend work of Swinnerton-Dyer on the density of the number of twists of a given elliptic curve that have 2-Selmer group of a particular rank.
Distributed proofs are mechanisms enabling the nodes of a network to collectivity and efficiently check the correctness of Boolean predicates on the structure of the network, or on data-structures distributed over the nodes (e.g., spanning…
Inspired by the analogy between the group of units $\mathbb{F}_p^{\times}$ of the finite field with $p$ elements and the group of points $E(\mathbb{F}_p)$ of an elliptic curve $E/\mathbb{F}_p$, E. Kowalski, A. Akbary & D. Ghioca, and T.…
Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the fibre result of Beresnevich, Haynes, and Velani. To achieve this, we prove an effective…
We give uniform proofs of tightness and exponential tightness of the sequences of stationary queue lengths in generalised Jackson networks in a number of setups which concern large, normal and moderate deviations.
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more efficient than current implementation as the conductor of…
It is known, that for every elliptic curve over Q there exists a quadratic extension in which the rank does not go up. For a large class of elliptic curves, the same is known with the rank replaced by the 2-Selmer group. We show, however,…
Given a web (multi-foliation) and a linear system on a projective surface we construct divisors cutting out the locus where some element of the linear system has abnormal contact with the leaf of the web. We apply these ideas to reobtain a…
We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…
We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of…
In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.
We consider the problem of bounding the dimension of the linear system of curves in ${\bf P}^2$ of degree $d$ with prescribed multiplicities $m_1,...,m_n$ at $n$ general points (\cite{Hir1},\cite{Hir2}). We propose a new method, based on…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…
In this paper, we study tame Galois coverings of semistable models that arise from torsion points on elliptic curves. These coverings induce Galois morphisms of intersection graphs and we express the decomposition groups of the edges in…
A cycle of elliptic curves is a list of elliptic curves over finite fields such that the number of points on one curve is equal to the size of the field of definition of the next, in a cyclic way. We study cycles of elliptic curves in which…
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…
The main purpose of this paper is the geometric construction, and the analysis of the formalism of elliptic Bloch groups. In the setting of absolute cohomology, we obtain a generalization of Beilinson's Eisenstein symbol to divisors of an…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…