D. Tolev

activity

20042017

most citedAn invitation to additive prime number theory

20 citations · 35 across the 11 of their papers we have counts for

collaborators

12 papers

math.NT2017★ 2 cited

On a diophantine inequality with prime numbers of a special type

D. I. Tolev

We consider the Diophantine inequality \[ \left| p_1^{c} + p_2^{c} + p_3^c- N \right| < (\log N)^{-E} , \] where $1 < c < \frac{15}{14}$ , $N$ is a sufficiently large real number an…

math.NT2016

On an equation involving fractional powers with one prime and one almost prime variables

Zhivko Petrov, Doychin Tolev

In this paper we consider the equation $[p^{c}] + [m^{c}] = N$ , where $N$ is a sufficiently large integer, and prove that if $1 < c < \frac{29}{28}$ , then it has a solution in a pr…

math.NT2013★ 1 cited

On the equation $x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} = N$ with variables such that $x_{1} x_{2} x_{3} x_{4} + 1$ is an almost-prime

T. L. Todorova, D. I. Tolev

We consider Lagrange's equation $x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} = N$ , where $N$ is a sufficiently large and odd integer, and prove that it has a solution in natural numbers $x_1, \d…

math.NT2011

On the remainder term in the circle problem in an arithmetic progression

D. I. Tolev

In this paper we improve the estimate for the remainder term in the asymptotic formula concerning the circle problem in an arithmetic progression.

math.NT2010★ 2 cited

An identity for the Kloosterman sum

D. I. Tolev

We establish a simple identity and using it we find a new proof of a result of Kloosterman.

math.NT2010★ 3 cited

On the number of pairs of positive integers $x, y \leq H$ such that $x^{2} + y^{2} + 1$ is squarefree

Doychin Tolev

It is not difficult to find an asymptotic formula for the number of pairs of positive integers $x, y \leq H$ such that $x^{2} + y^{2} + 1$ is squarefree. In the present paper we improve…

On a diophantine inequality with prime numbers of a special type

On an equation involving fractional powers with one prime and one almost prime variables

On the equation x12​+x22​+x32​+x42​=N with variables such that x1​x2​x3​x4​+1 is an almost-prime

On the remainder term in the circle problem in an arithmetic progression

An identity for the Kloosterman sum

On the number of pairs of positive integers x,y≤H such that x2+y2+1 is squarefree

On the equation $x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} = N$ with variables such that $x_{1} x_{2} x_{3} x_{4} + 1$ is an almost-prime

On the number of pairs of positive integers $x, y \leq H$ such that $x^{2} + y^{2} + 1$ is squarefree