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pro vyhledávání: '"D. I. Tolev"'
Autor:
D. I. Tolev
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 299:246-267
We consider the Diophantine inequality |p 1 + p 2 + p 3 − N| 0 is an arbitrarily large constant. We prove that the above inequality has a solution in primes p1, p2, p3 such that each of the numbers p1 + 2, p2 + 2 and p3 + 2 has at most [369/(180
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::af0d241b54ae2db87893cccc38a26d2d
https://doi.org/10.1134/s0081543817080168
https://doi.org/10.1134/s0081543817080168
Autor:
D. I. Tolev, Zhivko Petrov
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 298:38-56
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 prime $p$ and an almost prime $m$ with at most $\left[ \frac{52}{29 - 28
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f84a37238f0585f411a3367265dc341e
https://doi.org/10.1134/s0081543817070021
https://doi.org/10.1134/s0081543817070021
Autor:
D. I. Tolev, T. L. Todorova
Publikováno v:
Tatra Mountains Mathematical Publications. 59:1-26
We consider Lagrange’s equation x2 1 +x2 2 +x2 3 +x2 4 = N, where N is a sufficiently large and odd integer, and prove that it has a solution in natural numbers x1, . . . , x4 such that x1x2x3x4 + 1 has no more than 48 prime factors.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::623d932483f3d31419c602f7cb10d92d
https://doi.org/10.2478/tmmp-2014-0015
https://doi.org/10.2478/tmmp-2014-0015
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 280:1-22
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bf809983efebe2613eff3192fb46813e
https://doi.org/10.1134/s0081543813030012
https://doi.org/10.1134/s0081543813030012
Autor:
D. I. Tolev, T. L. Todorova
Publikováno v:
Mathematica Slovaca. 60:771-786
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 existenc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::484646530ff600c8abfb4d449c4f4c1c
https://doi.org/10.2478/s12175-010-0045-3
https://doi.org/10.2478/s12175-010-0045-3
Autor:
D. I. Tolev, A. Kirkoryan
Publikováno v:
Mathematical Notes. 88:365-373
We prove that almost all natural numbers n satisfying the congruence n ≡ 3 (mod 24), n ≢ 0 (mod 5), can be expressed as the sum of three squares of primes, at least one of which can be written as 1 + x2 + y2.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bef0ea48698c056036a484465eecac69
https://doi.org/10.1134/s0001434610090099
https://doi.org/10.1134/s0001434610090099
Autor:
D. I. Tolev
Publikováno v:
Monatshefte für Mathematik. 165:557-567
It is not difficult to find an asymptotic formula for the number of pairs of positive integers x, y ≤ H such that x2 + y2 + 1 is squarefree. In the present paper we improve the estimate for the error term in this formula using the properties of cer
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::13de6f18b09206867cfdb9c0657046ec
https://doi.org/10.1007/s00605-010-0246-4
https://doi.org/10.1007/s00605-010-0246-4
Autor:
D. I. Tolev
Publikováno v:
Journal of Number Theory. 130:439-457
We consider the ternary Goldbach problem with two prime variables of the form k 2 + m 2 + 1 and find an asymptotic formula for the number of its solutions.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a990e75f9bc9b8da86a2eb0a16477e39
https://doi.org/10.1016/j.jnt.2009.07.012
https://doi.org/10.1016/j.jnt.2009.07.012
Autor:
D. I. Tolev
Publikováno v:
The Quarterly Journal of Mathematics. 62:215-221
We establish Bombieri-Vinogradov's type result for the number of solutions of the ternary Goldbach problem with primes from arithmetic progressions.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6685ed00297448e7c7c028dabb8403cd
https://doi.org/10.1093/qmath/hap027
https://doi.org/10.1093/qmath/hap027
Autor:
D. I. Tolev
Publikováno v:
International Journal of Number Theory. :225-234
We consider the number of r-tuples of squarefree numbers in a short interval. We prove that it cannot be much bigger than the expected value and we also establish an asymptotic formula if the interval is not very short.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4d3b9a23b14df021a1da0a87d9944135
https://doi.org/10.1142/s179304210600053x
https://doi.org/10.1142/s179304210600053x