arXiv subjects

D. I. Tolev

Publications and source records attributed to D. I. Tolev.

6 recordsLinked to original sources

arXiv2017

On a diophantine inequality with prime numbers of a special type

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 and $E>0$ is an arbitrarily large constant. We prove that the above inequality has a solution in primes $p_1$, $p_2$, $p_3$ such that each of the numbers $p_1 + 2, p_2 + 2, p_3 + 2$ has at most $\left[ \frac{369}{180 - 168 c} \right]$ prime factors, counted with the multiplicity.

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arXiv2014

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

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, \dots, x_4 $ such that $x_1 x_2 x_3 x_4 + 1$ has no more than 48 prime factors.

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arXiv2011

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

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

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arXiv2010

An identity for the Kloosterman sum

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

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arXiv2007

On the distribution of αp modulo one for primes p of a special form

A classical problem in analytic number theory is to study the distribution of $αp$ modulo 1, where $α$ is irrational and $p$ runs over the set of primes. We consider the subsequence generated by the primes $p$ such that $p+2$ is an almost-prime (the existence of infinitely many such $p$ is another topical result in prime number theory) and prove that its distribution has a similar property.

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arXiv2004

An invitation to additive prime number theory

The main purpose of this survey is to introduce an inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.

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