Related papers: Quadratic Equations in Three Variables over Gaussi…
In this article, we show that the quartic Diophantine equations $x^4 \pm pqy^4=\pm z^2$ and $ x^4 \pm pq y^4= \pm iz^2$ have only trivial solutions for some primes $p$ and $q$ satisfying conditions $ p \equiv 3 \pmod 8, ~ q \equiv 1 \pmod 8…
We show arithmetic triplets of Gaussian squares are in 3-to-1 correspondence with Pythagorean triples thereof. This correspondence would transform a solution to the Magic Square of Squares puzzle into a larger structure of perfect Gaussian…
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
We present bounds of quadratic form for the logarithm of the Gaussian Q-function. We also show an analytical method for deriving log-quadratic approximations of the Q-function and give an approximation with absolute error less than…
We establish asymptotic formulae for the number of biquadratic number fields of bounded discriminant that can be embedded into a quaternionic or a dihedral extension. To prove these results, we express the solvability of these inverse…
For a finitely generated group $G$, the \emph{Diophantine problem} over $G$ is the algorithmic problem of deciding whether a given equation $W(z_1,z_2,\ldots,z_k) = 1$ (perhaps restricted to a fixed subclass of equations) has a solution in…
We study the physical content of quadratic diff-invariant Lagrangians in arbitrary dimensions by using covariant symplectic techniques. This paper extends previous results in dimension four. We discuss the difference between the even and…
The paper investigates some aspects of the geometry and the arithmetic of a non-rigid Calabi-Yau threefold. Particular emphasis is given to the study of its L-function L(H^3,s) and the Galois representation.
We evaluate the enumerative invariants of low degree on the mirror quintic threefold.
In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
This article generalizes the geometric quadratic Chabauty method, initiated over $\mathbb{Q}$ by Edixhoven and Lido, to curves defined over arbitrary number fields. The main result is a conditional bound on the number of rational points on…
In this short note we present a method of solving this Diophantine equation, method which is different from Ljunggren's, Mordell's, and R.K.Guy's.
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
It has been established on many occasions that the set of quotients of prime numbers is dense in the set of positive real numbers. More recently, it has been proved that the set of quotients of primes in the Gaussian integers is dense in…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
Let $A\subset \N_{+}$ and by $P_{A}(n)$ denotes the number of partitions of an integer $n$ into parts from the set $A$. The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations…
In this paper we find a parametric solution to the hitherto unsolved problem of finding three positive integers such that their sum, the sum of their squares and the sum of their cubes are simultaneously perfect squares.
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…