On the simultaneous representation of numbers as a sum of prime numbers
https://doi.org/10.22405/2226-8383-2026-27-1-4-18
Abstract
In the paper, we estimate the cardinality of the set of positive integers 1 ⩽ 𝑏1, 𝑏2, . . . , 𝑏𝑠 ⩽ 𝑋 satisfying to the conditions of congruent-solvability and positive solvability, and of the exceptional set in the problem of simultaneous representation of 𝑠 numbers 𝑏1, 𝑏2, . . . , 𝑏𝑠 the sums of 𝑚(𝑠 < 𝑚 < 2𝑠) primes. We also obtain a new lower estimate for the number of such representations.
Keywords
system of linear equations,
asymptotic formula,
power estimate,
congruent solvability,
positive solvability,
Dirichlet character,
principal Dirichlet character,
Dirichlet 𝐿−function,
exceptional character,
exceptional zero,
Mangoldt function,
minor arcs,
major arcs„ singular series,
singular integral.
About the Authors
Ismail Allakov
Termez State University
Uzbekistan
Uzbekistan
doctor of physical and mathematical sciences, professor
Bekmurod Kholboy ugli Erdonov
Termez University of Economics and Service
Uzbekistan
Uzbekistan
doctor of philosophy (PhD) in physical and mathematical sciences
Oybek Shanazarovich Imamov
Termez State University
Uzbekistan
Uzbekistan
lecturer
References
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Review
For citations:
Allakov I., Erdonov B.Kh., Imamov O.Sh. On the simultaneous representation of numbers as a sum of prime numbers. Chebyshevskii Sbornik. 2026;27(1):4-18. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-1-4-18
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