Romeo Mevstrovi'c

activity

20122019

most citedEuclid's theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.--2022) and another new proof

13 citations · 48 across the 20 of their papers we have counts for

collaborators

20 papers

math.NT2019

Closed maximal ideals ideals in some Fréchet algebras of holomorphic functions

Romeo Meštrović

The space $F^{p}$ ( $1 < p < \infty$ ) consists of all holomorphic functions $f$ on the open unit disk $D$ such that $lim_{r \to 1} (1 - r)^{1/ q} lo g^{+} M_{\infty} (r, f) = 0,$ where $M_{\inf…

math.CV2019★ 1 cited

A characterization of some prime ideals in certain $F$ -algebras of holomorphic functions

Romeo Meštrović

The class $M^{p}$ $(1 < p < \infty)$ consists of all holomorphic functions $f$ on the open unit disk $D$ for which $\int_{0}^{2 π} (lo g^{+} M f (θ))^{p} \frac{d θ}{2 π} < \infty,$ …

math.NT2019

Goldbach's like conjectures arising from arithmetic progressions whose first two terms are primes

Romeo Meštrović

For two odd primes $p$ and $q$ such that $p < q$ , let $A (p, q) := (a_{k})_{k = 1}^{\infty}$ be the arithmetic progression whose $k$ th term is given by $a_{k} = (k - 1) (q - p) + p$ (i.e., with $a_{1} = p$ …

math.NT2018

A characterization of maximal ideals in the Fréchet algebras of holomorphic functions $F^{p}$ $(1 < p < \infty$

Romeo Meštrović

The space $F^{p}$ ( $1 < p < \infty$ ) consists of all holomorphic functions $f$ on the open unit disk $D$ for which $lim_{r \to 1} (1 - r)^{1/ q} lo g^{+} M_{\infty} (r, f) = 0,$ where $M_{\inft…

math.FA2018

On some metric topologies on Privalov spaces on the unit disk

Romeo Meštrović, Žarko Pavićević

Let $N^{p}$ $(1 < p < \infty)$ be the Privalov class $N^{p}$ of holomorphic functions on the open unit disk $D$ in the complex plane. In 1977 M. Stoll proved that the class $N^{p}$ equi…

eess.SP2018★ 4 cited

A generalization of some random variables involving in certain compressive sensing problems

Romeo Meštrović

In this paper we give a generalization of the discrete complex-valued random variable defined and investigated in \cite{ssa} and \cite{m8}. We prove the statements concerning the e…

math.NT2018

On the distribution of primes in the alternating sums of concecutive primes

Romeo Meštrović

Quite recently, in [8] the authoor of this paper considered the distribution of primes in the sequence $(S_{n})$ whose $n$ th term is defined as $S_{n} = \sum_{k = 1}^{2 n} p_{k}$ , where $p_{k}$ …

math.CV2018★ 5 cited

Ideals in some Rings of Nevanlinna-Smirnov Type

Romeo Meštrović

Let $N^{p}$ $(1 < p < \infty)$ denote the algebra of holomorphic functions in the open unit disk, introduced by I.~I.~Privalov with the notation $A_{q}$ in [8]. Since $N^{p}$ becomes a ring…

math.NT2018★ 1 cited

Curious conjectures on the distribution of primes among the sums of the first $2 n$ primes

Romeo Meštrović

Let $p_{n}$ be $n$ th prime, and let $(S_{n})_{n = 1}^{\infty} := (S_{n})$ be the sequence of the sums of the first $2 n$ consecutive primes, that is, $S_{n} = \sum_{k = 1}^{2 n} p_{k}$ with $n=1,2,\ldots…

math.FA2018★ 1 cited

Remarks on Generalized Hardy Algebras

Romeo Meštrović, Žarko Pavićević, Novo Labudović

For a measure space $(Ω, Σ, μ)$ with a positive finite measure $μ$ , and a positive real number $p$ , we define the space $L_{p}^{+} (μ) = L_{p}^{+}$ of all (equivalence classes of) $Σ$ -mea…

math.CO2018★ 2 cited

Different classes of binary necklaces and a combinatorial method for their enumerations

Romeo Meštrović

In this paper we investigate enumeration of some classes of $n$ -character strings and binary necklaces. Recall that binary necklaces are necklaces in two colors with length $n$ . We…

math.PR2018★ 1 cited

On some random variables involving Bernoulli random variable

Romeo Meštrović

Motivated by the recent investigations given in [25] and the fact that Bernoulli probability-type models were often used in the study on some problems in theory of compressive sens…

math.PR2018★ 3 cited

A note on some sub-Gaussian random variables

Romeo Meštrović

In [8] the author of this paper continued the research on the complex-valued discrete random variables $X_{l} (m, N)$ ( $0 \leq l \leq N - 1$ , $1 \leq M \leq N)$ recently introduced and studied i…

math.ST2018★ 4 cited

On some discrete random variables arising from recent study on statistical analysis of compressive sensing

Romeo Meštrović

The recent paper [27] provides a statistical analysis for efficient detection of signal components when missing data samples are present. Here we focus our attention to some comple…

math.NT2014★ 9 cited

Lucas' theorem: its generalizations, extensions and applications (1878--2014)

Romeo Meštrović

In 1878 É. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient $(m n)$ modulo a prime $p$ in terms of the binomial coefficients…

math.NT2014★ 1 cited

Variations of Kurepa's left factorial hypothesis

Romeo Meštrović

Kurepa's hypothesis asserts that for each integer $n \geq 2$ the greatest common divisor of $! n := \sum_{k = 0}^{n - 1} k!$ and $n!$ is $2$ . Motivated by an equivalent formulation of this h…

math.NT2013★ 1 cited

Generalizations of Carmichael numbers I

Romeo Meštrović

A composite positive integer $n$ is said to be a {\it weak Carmichael number} if $$ \sum_{\gcd(k,n)=1\atop 1\le k\le n-1}k^{n-1}\equiv φ(n) \pmod{n}. \leqno(1) $$ It is proved that…

math.NT2012★ 2 cited

An elemetary proof of an estimate for a number of primes less than the product of the first $n$ primes

Romeo Meštrović

Let $α$ be a real number such that $1 < α < 2$ and let $x_{0} = x_{0} (α)$ be a {\rm(}unique{\rm)} positive solution of the equation $x^{α - 1} - \frac{π}{e ^{2} 3} x + 1 = 0.$ Then we prove t…

math.NT2012

A congruence modulo $n^{3}$ involving two consecutive sums of powers and its applications

Romeo Meštrović

For various positive integers $k$ , the sums of $k$ th powers of the first $n$ positive integers, $S_{k} (n + 1) = 1^{k} + 2^{k} + ... + n^{k}$ , have got to be some of the most popular sums in all of m…

math.HO2012★ 13 cited

Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.--2022) and another new proof

Romeo Meštrović

{\bf In the fourth extended version of this article, we provide a comprehensive historical survey of 200 different proofs of famous Euclid's theorem on the infinitude of prime numb…

Closed maximal ideals ideals in some Fréchet algebras of holomorphic functions

A characterization of some prime ideals in certain F-algebras of holomorphic functions

Goldbach's like conjectures arising from arithmetic progressions whose first two terms are primes

A characterization of maximal ideals in the Fréchet algebras of holomorphic functions Fp (1<p<∞

On some metric topologies on Privalov spaces on the unit disk

A generalization of some random variables involving in certain compressive sensing problems

On the distribution of primes in the alternating sums of concecutive primes

Ideals in some Rings of Nevanlinna-Smirnov Type

Curious conjectures on the distribution of primes among the sums of the first 2n primes

Remarks on Generalized Hardy Algebras

Different classes of binary necklaces and a combinatorial method for their enumerations

On some random variables involving Bernoulli random variable

A note on some sub-Gaussian random variables

On some discrete random variables arising from recent study on statistical analysis of compressive sensing

Lucas' theorem: its generalizations, extensions and applications (1878--2014)

Variations of Kurepa's left factorial hypothesis

Generalizations of Carmichael numbers I

An elemetary proof of an estimate for a number of primes less than the product of the first n primes

A congruence modulo n3 involving two consecutive sums of powers and its applications

Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.--2022) and another new proof

A characterization of some prime ideals in certain $F$ -algebras of holomorphic functions

A characterization of maximal ideals in the Fréchet algebras of holomorphic functions $F^{p}$ $(1 < p < \infty$

Curious conjectures on the distribution of primes among the sums of the first $2 n$ primes

An elemetary proof of an estimate for a number of primes less than the product of the first $n$ primes

A congruence modulo $n^{3}$ involving two consecutive sums of powers and its applications