Related papers: Some multiplicative functions over $\mathbb{F}_2$

Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…

In [Tha15], we looked at two (`multiplicative' and `Carlitz-Drinfeld additive') analogs each, for the well-known basic congruences of Fermat and Wilson, in the case of polynomials over finite fields. When we look at them modulo higher…

Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…

This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…

We consider two number-theoretic problems arising from Fuglede's spectral set conjecture: characterizing finite sets that tile integers, and finding polynomials with (0,1) coefficients whose roots have a certain multiplicative structure. We…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

We investigate whether the group algebra of a finite group over a localisation of the integers is semiperfect. The main result is a necessary and sufficient arithmetic criterion in the ordinary case. In the modular case, we propose a…

We design new tools to study variants of Total Dual Integrality. As an application, we obtain a geometric characterization of Total Dual Integrality for the case where the associated polyhedron is non-degenerate. We also give sufficient…

We introduce a simple sieve-theoretic approach to studying partial sums of multiplicative functions which are close to their mean value. This enables us to obtain various new results as well as strengthen existing results with new proofs.…

In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire…

We generalize the definition of spoof perfect numbers to multiperfect numbers and study their characteristics. As a result, we find several new odd spoof multiperfect numbers, akin to Descartes' number. An example is $8999757$, which would…

We present lower bounds on the sum and product of the distinct prime factors of an odd perfect number, which provide a lower bound on the size of the odd perfect number as a function of the number of its distinct prime factors.

Permutation polynomials over finite fields have taken an important role in vast areas in mathematics as well as engineering. Recently, Tu et al. gave some classes of complete permutation polynomials over finite fields of even…

We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two and…

Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…

We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…

Let $\sigma(n)$ be the sum of the positive divisors of $n$. A number $n$ is said to be 2-near perfect if $\sigma(n) = 2n +d_1 +d_2 $, where $d_1$ and $d_2$ are distinct positive divisors of $n$. We give a complete description of those $n$…

Necessary and sufficient conditions for a finite connected graph with a strict partial order on vertices to be a combinatorial invariant of pseudoharmonic function are obtained.

Let $X$ be a noncomplete metric space satisfying the usual (local) assumptions of a doubling property and a Poincar\'e inequality. We study extensions of Newtonian Sobolev functions to the completion $\widehat{X}$ of $X$ and use them to…

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…