S. Dimitrov

activity

20172022

most citedA logarithmic inequality involving prime numbers

3 citations · 10 across the 13 of their papers we have counts for

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math.NT2022★ 2 cited

Exponential sums over Piatetski-Shapiro primes in arithmetic progressions

S. I. Dimitrov

Let $γ < 1 < c$ and $19 (c - 1) + 171 (1 - γ) < 9$ . In this paper, we establish an asymptotic formula for exponential sums over Piatetski-Shapiro primes $p = [n^{1/ γ}]$ in arithmetic progressions.

math.NT2021

On an tangent equation by primes

S. I. Dimitrov

In this paper we introduce a new diophantine equation with prime numbers. Let $[\cdot]$ be the floor function. We prove that when $1 < c < \frac{23}{21}$ and $θ > 1$ is a fixed, the…

math.NT2021

Prime numbers of the form $[n^{c} ta n^{θ} (logn)]$

S. I. Dimitrov

Let $[\cdot]$ be the floor function. In the present paper we prove that when $1 < c < \frac{12}{11}$ and $θ > 1$ is a fixed, then there exist infinitely many prime numbers of the fo…

math.NT2021

A tangent inequality over primes

S. I. Dimitrov

In this paper we introduce a new diophantine inequality with prime numbers. Let $1 < c < \frac{10}{9}$ . We show that for any fixed $θ > 1$ , every sufficiently large positive number $N$ a…

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.NT2019

On an logarithmic equation by primes

S. I. Dimitrov

Let $[\cdot]$ be the floor function. In this paper we show that every sufficiently large positive integer $N$ can be represented in the form \begin{equation*} N=[p_1\log p_1]+…

Exponential sums over Piatetski-Shapiro primes in arithmetic progressions

On an tangent equation by primes

Prime numbers of the form [nctanθ(logn)]

A tangent inequality over primes

Diophantine approximation by Piatetski-Shapiro primes

On an logarithmic equation by primes

Prime numbers of the form $[n^{c} ta n^{θ} (logn)]$