Blazej Zmija

activity

20172026

most citedReal quadratic fields with a universal quadratic form of given rank have density zero

4 citations · 4 across the 12 of their papers we have counts for

collaborators

13 papers

math.CO2026

Submultiplicative Polynomials in Combinatorics

Krystian Gajdzica, Bernhard Heim, Markus Neuhauser +1

For normalized sequences $(g (n))_{n \in N}$ we consider recursively defined polynomials $P_{n}^{g} (x)$ . In this paper we study their submultiplicative property, viewe…

math.NT2025

Large gaps between values of several binary quadratic forms

Błażej Żmija

In this paper we study the problem of long gaps between values of binary quadratic forms. Let $D_{1}$ , $D_{2}, \dots, D_{r}$ be negative integers and $(s_{n})_{n = 1}^{\infty}$ be th…

math.NT2025

Counting polynomials with positive roots

Pavlo Yatsyna, Błażej Żmija

This paper investigates the number of monic integer polynomials of degree $n$ whose roots are all real and positive. We establish an asymptotic formula for the case of fixed trace…

math.CA2025

Bounded ranges of cardinal functions

Jacek Marchwicki, Błażej Żmija

Let $x$ be a (non-empty) sequence of positive real numbers. Its achievement set $x$ is the set of all the possible sums of the elements of $x$ .…

math.NT2025

Kitaoka's Conjecture for quadratic fields

Vitezslav Kala, Jakub Krásenský, Dayoon Park +2

We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic…

math.CO2024

Connections between certain numbers related to derangements and $r$ -permutations

Piotr Miska, Błażej Żmija

For non-negative integer parameters $r, u, m, n$ define \begin{align*} \cal{D}(r,u,m,n) := \big\{\ σ\in \cal{S}_{r+n}\ \big|\ σ(x)=y \textrm{ for exactly } u \textrm{ pairs } (x,y) \t…

math.CO2024

$M$ -ary partition polynomials

Błażej Żmija

Let $M = (m_{i})_{i = 0}^{\infty}$ be a sequence of integers such that $m_{0} = 1$ and $m_{i} \geq 2$ for $i \geq 1$ . In this paper we study $M$ -ary partition polynomials $(p_{M}(n,t))_{n=…

math.NT2024

High order congruences for $M$ -ary partitions

Błażej Żmija

For a sequence $M = (m_{i})_{i = 0}^{\infty}$ of integers such that $m_{0} = 1$ , $m_{i} \geq 2$ for $i \geq 1$ , let $p_{M} (n)$ denote the number of partitions of $n$ into parts of the form…

math.NT2023★ 4 cited

Real quadratic fields with a universal quadratic form of given rank have density zero

Vitezslav Kala, Pavlo Yatsyna, Błażej Żmija

We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More gene…

math.NT2019

A note on primes with prime indices

Błażej Żmija

Let $n, k \in N$ and let $p_{n}$ denote the $n$ th prime number. We define $p_{n}^{(k)}$ recursively as $p_{n}^{(1)} := p_{n}$ and $p_{n}^{(k)} = p_{p_{n}^{(k - 1)}}$ , that is, $p_{…

math.NT2019

On distribution of subsequences of primes having prime indices with respect to the $(R)$ -denseness and convergence exponent

Piotr Miska, János T. Tóth, Błażej Żmija

Denote by $N$ and $P$ the set of all positive integers and prime numbers, respectively. Let $P = {p_{1} < p_{2} < \dots < p_{n} < \dots}$ , where $p_{n}$ is the $n$ -th p…

math.NT2018

A new upper bound for numbers with the Lehmer property and its application to repunit numbers

Dominik Burek, Błażej Żmija

A composite positive integer $n$ has the Lehmer property if $ϕ (n)$ divides $n - 1,$ where $ϕ$ is an Euler totient function. In this note we shall prove that if $n$ has the Lehmer pro…

math.NT2017

Recurrence sequences connected with the $m$ --ary partition function and their divisibility properties

Błażej Żmija

In this paper we introduce a class of sequences connected with the $m$ --ary partition function and investigate their congruence properties. In particular, we get facts about the se…

Submultiplicative Polynomials in Combinatorics

Large gaps between values of several binary quadratic forms

Counting polynomials with positive roots

Bounded ranges of cardinal functions

Kitaoka's Conjecture for quadratic fields

Connections between certain numbers related to derangements and r-permutations

M-ary partition polynomials

High order congruences for M-ary partitions

Real quadratic fields with a universal quadratic form of given rank have density zero

A note on primes with prime indices

On distribution of subsequences of primes having prime indices with respect to the (R)-denseness and convergence exponent

A new upper bound for numbers with the Lehmer property and its application to repunit numbers

Recurrence sequences connected with the m--ary partition function and their divisibility properties

Connections between certain numbers related to derangements and $r$ -permutations

$M$ -ary partition polynomials

High order congruences for $M$ -ary partitions

On distribution of subsequences of primes having prime indices with respect to the $(R)$ -denseness and convergence exponent

Recurrence sequences connected with the $m$ --ary partition function and their divisibility properties