Autors: Dimitrov, S. I.
Title: A ternary diophantine inequality by primes with one of the form p=x^2+y^2+1
Keywords: Diophantine inequality, Exponential sum, Bombieri -- Vinogra

Abstract: In this paper we solve the ternary Piatetski-Shapiro inequality with prime numbers of a special form. More precisely we show that, for any fixed $10$, the diophantine inequality \begin{equation*} |p_1^c+p_2^c+p_3^c-N|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3$, such that $p_1=x^2 + y^2 +1$. For this purpose we establish a new Bombieri -- Vinogradov type result for exponential sums over primes.

References

    Issue

    , vol. 59, issue 2, pp. 571 – 607, 2022, Netherlands, Ramanujan J., https://doi.org/10.1007/s11139-021-00545-1

    Цитирания (Citation/s):
    1. Liu Y., On a Diophantine equation involving one Linnik prime, 2025, Ramanujan Journal, issue 2, vol. 68, DOI 10.1007/s11139-025-01191-7, issn 13824090, eissn 15729303 - 2025 - в издания, индексирани в Scopus
    2. Zhu L., On a ternary diophantine inequality with prime numbers of a special type II, 2025, Periodica Mathematica Hungarica, issue 1, vol. 90, pp. 35-56, DOI 10.1007/s10998-024-00602-4, issn 00315303, eissn 15882829 - 2025 - в издания, индексирани в Scopus
    3. Liu Y., On a quinary Diophantine inequality involving one prime of the special form, 2025, Ramanujan Journal, issue 2, vol. 66, DOI 10.1007/s11139-025-01027-4, issn 13824090, eissn 15729303 - 2025 - в издания, индексирани в Scopus
    4. Liu Y., On a ternary Diophantine inequality with one prime of the form p=x2+y2+1, 2025, Ramanujan Journal, issue 1, vol. 66, pp. 1-16, DOI 10.1007/s11139-024-00986-4, issn 13824090, eissn 15729303 - 2025 - в издания, индексирани в Scopus

    Вид: статия в списание, публикация в издание с импакт фактор, индексирана в Scopus