Related papers: Kurepa's conjecture on the left factorial function…

We prove a conjecture of the first author for $GL_2(F)$, where $F$ is a finite extension of $Q_p$.

We consider Fujita's freeness conjecture in a relative setting and prove a criterion by proving a correct Q-divisor version of the Kollar vanishing theorem.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

We prove the Aharoni Berger Conjecture

In this paper we prove the WALA conjecture.

We prove the factorization conjecture for triple-product $p$-adic $L$-functions formulated in a companion article in the special case when two of the (three) factors have complex multiplication.

We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.

We investigate the existence of primes $p > 5$ for which the residues of $2!$, $3!$, \dots, $(p-1)!$ modulo $p$ are all distinct. We describe the connection between this problem and Kurepa's left factorial function, and report that there…

We establish an invertibility criterion for free polynomials and free functions evaluated on some tuples of matrices. We show that if the derivative is nonsingular on some domain closed with respect to direct sums and similarity, the…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

In this paper we consider the functional equation for alternating factorial sum and some of its particular solutions (alternating Kurepa's function $A(z)$ from [Petojevic_02] and function $A_{1}(z)$). We determine an extension of domain of…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

Extending Gross's result, we prove that a certain factorizaton of measures holds for all $p$ and any finite even Dirichlet character $\chi$ of any conductor, rather than only for split $p$ and $\chi$ with conductor a power of $p$. Using…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument. We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler…

In this paper we consider the functional equation for factorial sum and its particular solutions (Kurepa's function $K(z)$ \cite{Kurepa_71} and function $K_{1}(z)$). We determine an extension of domain of functions $K(z)$ and $K_{1}(z)$ in…

The Image Conjecture was formulated by the third author, who showed that it implied his Vanishing Conjecture, which is equivalent to the famous Jacobian Conjecture. We prove various cases of the Image Conjecture and show how it leads to…

This paper examines the algebraic features of notable polynomial functions and explores their combinatorial aspects by presenting precise decompositions in terms of Dobinski numbers, Bell numbers, and moments generating functions.…

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

In our previous works we found a power series expansion of a particular case of Fox's $H$ function $H^{q,0}_{p,q}$ in a neighborhood of its positive singularity. An inverse factorial series expansion of the integrand of $H^{q,0}_{p,q}$…