Related papers: Arithmetics in number systems with cubic base
We present new results on finite satisfiability of logics with counting and arithmetic. One result is a tight bound on the complexity of satisfiability of logics with so-called local Presburger quantifiers, which sum over neighbors of a…
In [25], T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the $\mathbf n$-$t$-quasi-greedy property that is based on them. Building upon this foundation, our…
We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units.…
A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We…
The goal is to obtain an asymptotic formula for the number of quadratic extensions with bounded discriminant of a some quadratic number field with odd class number. This extends an already known result for Q.
We investigate cases where Thabit and Williams numbers in base $b$ can be expressed as the sum or difference of two $g$-repdigits. For specific values of $b$ and $g$, we describe parametric solutions yielding infinitely many solutions for…
Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estimates on average over arithmetic progressions are…
We define and study a transform whose iterates bring to the fore interesting relations between Pisot numbers and primes. Although the relations we describe are general, they take a particular form in the Pisot limit points. We give three…
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…
Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
We establish the existence of a quantum lift of the greedy basis.
One of the main themes in this thesis is the description of the signature of both the infinite place and the finite places in cubic function fields of any characteristic and quartic function fields of characteristic at least 5. For these…
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to…
The goal of this thesis is to investigate the structural properties of certain sequential problems in order to bring the solutions closer to a practical use. In the first part, we put a special emphasis on structures that can be represented…
An expansion upon Donald Kunth's quarter-imaginary base system is introduced to handle any imaginary number base where its real part is zero and the absolute value of its imaginary part is greater than one. A brief overview on number bases…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…