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Chebyshevskii Sbornik, 2022, Volume 23, Issue 2, Pages 21–41
DOI: https://doi.org/10.22405/2226-8383-2022-23-2-21-41 (Mi cheb1175) 		 
New estimates for the exceptional set of the sum of two primes from an arithmetic progression

I. Allakov, A. Sh. Safarov

Termez State University (Uzbekistan, Termez)
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DOI: https://doi.org/10.22405/2226-8383-2022-23-2-21-41
Abstract: The paper studies the question of representing numbers as the sum of two primes from an arithmetic progression, that is, the binary Goldbach problem, when primes are taken from an arithmetic progression. New estimates are proved for the number of even natural numbers that are (possibly) not representable as a sum of two primes from an arithmetic progression and for a number representing a given natural number, as a sum of two primes from an arithmetic progression.
Keywords: The Dirichlet charakter, Dirichlet $L$-function, exceptional set, representation numbers,exceptional zero, exceptional nature, main member, remaining member.
Received: 17.09.2021
Accepted: 22.06.2022
Document Type: Article
UDC: 511.2
Language: Russian
Citation: I. Allakov, A. Sh. Safarov, “New estimates for the exceptional set of the sum of two primes from an arithmetic progression”, Chebyshevskii Sb., 23:2 (2022), 21–41
Citation in format AMSBIB
\Bibitem{AllSaf22}
\by I.~Allakov, A.~Sh.~Safarov
\paper New estimates for the exceptional set of the sum of two primes from an arithmetic progression
\jour Chebyshevskii Sb.
\yr 2022
\vol 23
\issue 2
\pages 21--41
\mathnet{http://mi.mathnet.ru/cheb1175}
\crossref{https://doi.org/10.22405/2226-8383-2022-23-2-21-41}
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