This paper considers the problem of representing a given natural number as combination of two prime numbers and the square of a third prime number taken from an arithmetic progression. It was the rst to establish the solvability of the equation under consideration in prime numbers from the arithmetic progression, and prove a lower estimate for the number of solutions to this equation. The results obtained are important in the study of additive problems with prime numbers. The proof of the obtained results uses the Hardy-Littlewood circular method and the Vinogradov method of trigonometric sums.
| Mualliflar | Imamov, Oybek |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-1-8 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-8 · Maqolaning asl sahifasi
diophantine equation; congruent solution; exceptional zero; Dirichlet L-function; prin cipal characters; Legendre symbol; minor arc; major arc; singular series; singular integral.
| APA | Imamov, Oybek (2026). On representations of a given number as the sum of two primes and the square of a third prime in an arithmetic progression. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-8 |
|---|---|
| GOST (OAK) | Imamov, Oybek On representations of a given number as the sum of two primes and the square of a third prime in an arithmetic progression // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-8. |
| MLA | Imamov, Oybek. “On representations of a given number as the sum of two primes and the square of a third prime in an arithmetic progression.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-8 |
| Chicago | Imamov, Oybek. “On representations of a given number as the sum of two primes and the square of a third prime in an arithmetic progression.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-8 |
| Harvard | Imamov, Oybek (2026) ‘On representations of a given number as the sum of two primes and the square of a third prime in an arithmetic progression’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-8 |
| BibTeX | @article{imamovoybek2026,
title = {On representations of a given number as the sum of two primes and the square of a third prime in an arithmetic progression},
author = {Imamov, Oybek},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-8},
url = {https://doi.org/10.29229/uzmj.2026-1-8}
} |
Boshqa maqola uchun iqtibos tayyorlash
In this paper, a real analogue of a quasitrace is given, and its connection with the quasitrace of the enveloping C*-algebra is found.Similar to the complex case, some interesting properties of a quasitrace and the…
In this paper, we consider the two-state Hard-Core model on the closed Cayley tree of branching ratio two. On the symmetric case, we exactly solve the model and show that there is a phase transition.
In this paper, we present exact solution of haploid Markov chain model that describes the fluctuation of gene frequency under the influence of mutation. Also generalizing Markov chain model we introduce and investigate…
In this paper, we address the construction of an optimal quadrature formula in the sense of Sard within a Hilbert space composed of periodic, complex-valued functions, specifically for the purpose of numerically…
This paper discusses the frequent occurrence of the Hadamard type integral equation of the first kind in solving problems in aerodynamics, fluid dynamics, wave propagation theory, and ecology. Since the exact solution…
This paper proposes a method for solving the problems of the Euler - Bernoulli beam, in which the problem is reduced to the solution of the Fredholm integral equation of the second kind. This integral equation is solved…
The general operadic approach to splitting algebraic operations was developed in [1]. By splitting the product in a given algebraic variety $\mathcal{C}$, notion of $\mathcal{C}$-dendriform algebras was systematically…
This paper is devoted to the study of the geometric structure of neutral strongly facially symmetric (SFS) spaces, which provide a natural framework for modeling aspects of quantum mechanics in geometric terms. We…
Hamilton systems play a fundamental role in mechanics and mathematics, which usually generated by Hamiltonian vector fields.The geometry and topology of vector field orbits is not only an important branch of modern…
In this work, the problem of stabilizing the equilibrium state for a hyperbolic system with negative nonlocal characteristic velocities and measurement error is investigated. A mixed problem is considered for such…
O‘zbekiston matematika jurnali — barcha maqolalar · 2026-yil arxivi
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.