S. Dimitrov

activity

20162023

most citedA logarithmic inequality involving prime numbers

3 citations · 18 across the 30 of their papers we have counts for

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Showing 2020Show all

5 papers · 1 filter

math.NT2020

The quaternary Piatetski-Shapiro inequality with one prime of the form $p = x^{2} + y^{2} + 1$

S. I. Dimitrov

In this paper we show that, for any fixed $1 < c < 967/805$ , every sufficiently large positive number $N$ and a small constant $ε > 0$ , the diophantine inequality \begin{equati…

math.NT2020

A Bombieri -- Vinogradov type result for exponential sums over Piatetski-Shapiro primes

S. I. Dimitrov

In this paper, we establish a theorem of Bombieri -- Vinogradov type for exponential sums over Piatetski-Shapiro primes $p = [n^{1/ γ}]$ with $\frac{865}{886} < γ < 1$ .

math.NT2020

Diophantine approximation by Piatetski-Shapiro primes

S. I. Dimitrov

Let $[\cdot]$ be the floor function. In this paper we show that whenever $η$ is real, the constants $λ_{i}$ satisfy some necessary conditions, then for any fixed $1 < c < 38/37$ ther…

math.NT2020

Pairs of square-free values of the type $n^{2} + 1$ , $n^{2} + 2$

S. I. Dimitrov

In the present paper we show that there exist infinitely many consecutive square-free numbers of the form $n^{2} + 1$ , $n^{2} + 2$ . We also establish an asymptotic formula for the number o…

math.CO2020

On permutation patterns with constrained gap sizes

Stoyan Dimitrov

We consider avoidance of permutation patterns with designated gap sizes between pairs of consecutive letters. We call the patterns having such constraints distant patterns (DPs) an…

The quaternary Piatetski-Shapiro inequality with one prime of the form p=x2+y2+1

A Bombieri -- Vinogradov type result for exponential sums over Piatetski-Shapiro primes

Diophantine approximation by Piatetski-Shapiro primes

Pairs of square-free values of the type n2+1, n2+2

On permutation patterns with constrained gap sizes

The quaternary Piatetski-Shapiro inequality with one prime of the form $p = x^{2} + y^{2} + 1$

Pairs of square-free values of the type $n^{2} + 1$ , $n^{2} + 2$