Related papers: Finding an Ellipse Tangent to finitely many given …
This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
In this paper we study the inversion in an ellipse and some properties, which generalizes the classical inversion with respect to a circle. We also study the inversion in an ellipse of lines, ellipses and other curves. Finally, we…
In this note the following is shown. Consider the quadratic form on (complex) matrices Q(A):=tr(A^2). Let A be such a matrix. Then an ellipse can be found, with the vector from center to focus determined by the value of Q at the traceless…
This manuscript aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality. It can be seen as a bridge between an…
Consider a Jacobian elliptic surface $E \to C$ with a section $P$ of infinite order. Previous work of the first author and Urz\'ua over the complex numbers gives a bound on the number of tangencies between $P$ and a torsion section of $E$…
The entanglement of superpositions [Phys. Rev. Lett. 97, 100502 (2006)] is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed…
Several problems which could be thought of as belonging to recreational mathematics are described. They are all such that solutions to the problem depend on finding rational points on elliptic curves. Many of the problems considered lead to…
In this paper we construct parameterizations of elliptic curves over the rationals which have many consecutive integral multiples. Using these parameterizations, we perform searches in GMP and Magma to find curves with points of small…
Certain elliptic divisibility sequences are shown to contain only finitely many prime power terms. In certain circumstances, the methods show only finitely many terms have length below a given bound.
PhD Thesis--A compilation of the papers: "Lower Bounds for Identifying Codes in Some Infinite Grids", "Improved Bounds for r-identifying Codes of the Hex Grid", and "Vertex Identifying Codes for the n-dimensional Lattics" along with some…
The title says what is done here. Euler finds a news series for the arc of an ellipse. The paper is translated from the Latin original into German.
An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base…
By decision of the first author, the paper will no longer be available.
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…
The present review presents the authors previous results on the topic from the title in a new light. Most of the previous results were obtained using the techniques of antilinear Hilbert-Schmidt mappings of one Hilbert pace into another,…
Let R be a four-sided convex polygon in the xy plane and let M1 and M2 be the midpoints of the diagonals of R. It is well-known that if E is an ellipse inscribed in R, then the center of E must lie on Z, the open line segment connecting M1…
We present an elliptic version of Selberg's integral formula.
This paper briefly summarizes previous work on complex classical mechanics and its relation to quantum mechanics. It then introduces a previously unstudied area of research involving the complex particle trajectories associated with…
We present an explicit method to compute the (Siciak-Zaharjuta) extremal function of a real convex polytope in terms of supporting simplices and strips. We use this to give a new proof of the existence of extremal ellipses associated to the…