Results 81 to 90 of about 1,177 (152)

An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers

International Journal of Mathematics and Mathematical Sciences, 1990
We show that there exists a natural extention of the sum of divisors function to all unique factorization domains F having a finite number of units such that if a perfect number in F is defined to be an integer η whose proper divisors sum to η, then the ...
Wayne L. McDaniel
doaj   +1 more source

bk$b^k$‐Algebroids and the variety of foliation jets

Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.
Abstract We introduce and classify singular foliations of bk+1$b^{k+1}$‐type, which formalize the properties of vector fields that are tangent to a submanifold W⊂M$W \subset M$ to order k$k$. When W$W$ is a hypersurface, these structures are Lie algebroids generalizing the bk+1$b^{k+1}$‐tangent bundles introduced by Scott.
Francis Bischoff, Álvaro del Pino, Aldo Witte   +2 more
wiley   +1 more source

On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems

Axioms
This paper investigates bivariate vector-valued rational interpolation and recovery problems with common divisors in their denominators. By leveraging these shared divisors and employing a component-wise rational interpolation approach, we reduce the ...
Lixia Xiao, Peng Xia, Shugong Zhang
doaj   +1 more source

Bounded exponential sums with multiplicative coefficients

Mathematika, Volume 72, Issue 4, October 2026.
Abstract We investigate when the exponential sum Sf(x,α):=∑n⩽xf(n)e(nα)$S_f(x,\alpha) := \sum _{n\leqslant x}f(n)\mathrm{e}(n\alpha)$ is bounded, for a multiplicative function f$f$ and α∈R$\alpha \in \mathbb {R}$. We show that under natural assumptions, Sf(x,α)$S_f(x,\alpha)$ is bounded only when f$f$ is very close to a twisted Dirichlet character χ(n ...
Péa Bazin, Ihor Pylaiev, Fred Tyrrell
wiley   +1 more source

Abelian number fields with frobenian conditions

Mathematika, Volume 72, Issue 4, October 2026.
Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
wiley   +1 more source

An effective Bombieri–Vinogradov error term for sifting problems

Mathematika, Volume 72, Issue 4, October 2026.
Abstract In number theory, many major results related to the additive properties of primes are proven using the methods of sieve theory. However, in nearly every case, the existing proofs of these results are ineffective, in that explicit values for which they hold cannot be computed.
Daniel R. Johnston
wiley   +1 more source

The Divisors’ Hyperoperations

Ratio Mathematica, 2013
In the set N of the Natural Numbers we define two hyperoperations based on the divisors of the addition and multiplication of two numbers. Then, the properties of these two hyperoperations are studied together with the resulting hyperstructures ...
Achilles Dramalidis
doaj  

On weakly prime-additive numbers with length $4k+3$

Comptes Rendus. Mathématique
If a positive integer $n$ has at least two distinct prime divisors and can be written as $n=p_1^{\alpha _1}+\dots +p_t^{\alpha _t}$, where $p_13$, there exist infinitely many weakly prime-additive numbers $n$ with $m\mid n$ and $n=p_1^{\alpha _1}+\dots ...
Fang, Jin-Hui, Xue, Fang-Gang
doaj   +1 more source

Noncommutativity and noncentral zero divisors

International Journal of Mathematics and Mathematical Sciences, 1999
Let R be a ring, Z its center, and D the set of zero divisors. For finite noncommutative rings, it is known that D\Z≠∅. We investigate the size of |D\Z| in this case and, also, in the case of infinite noncommutative rings with D\Z≠∅.
Howard E. Bell, Abraham A. Klein
doaj   +1 more source

Some results concerning exponential divisors

International Journal of Mathematics and Mathematical Sciences, 1988
If the natural number n has the canonical form p1a1p2a2…prar then d=p1b1p2b2…prbr is said to be an exponential divisor of n if bi|ai for i=1,2,…,r. The sum of the exponential divisors of n is denoted by σ(e)(n). n is said to be an e-perfect number if σ(e)
Peter Hagis
doaj   +1 more source