Related papers: Beyond uniform cyclotomy
We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed…
In classical homotopy theory, two spaces are homotopy equivalent if one space can be continuously deformed into the other. This theory, however, does not respect the discrete nature of graphs. For this reason, a discrete homotopy theory…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing…
Let A={a_s(mod n_s)}_{s=0}^k be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results concerning system A. In particular, we show that if every integer lies in…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the…
The Gauss Circle Problem concerns finding asymptotics for the number of lattice point lying inside a circle in terms of the radius of the circle. The heuristic that the number of points is very nearly the area of the circle is surprisingly…
The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…
The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the…
We prove that the ideal used in recent works to categorify the cyclotomic integers is generated by a cyclotomic polynomial. Moreover, we publish a proof by T. Ekedahl that the $q$-binomial relations used in the tensor product of…
A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables.…
In decision theoretic estimation of parameters in Euclidean space $\mathbb{R}^p$, the action space is chosen to be the convex closure of the estimand space. In this paper, the concept has been extended to the estimation of circular…
In this paper, we provide details on the proofs of the quantum polynomial time algorithm of Biasse and Song (SODA 16) for computing the $S$-unit group of a number field. This algorithm directly implies polynomial time methods to calculate…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
We study the Euler-Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this…