Geodesic
On the exceptional set of the sum of a prime number and a fixed degree of a prime number
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 11-25

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Let $X$ be an enough big real number and let $M$ denote the set natural numbers not exceeding $X$ which cannot be written as a sum a prime and fixed degree of a prime number from arithmetical progression with a difference $d$. Let $E_d (X)=\mathrm{card}\, M.$ We obtain new a numerical sedate estimation for set $E_d (X)$ and an estimation from below for number presentation $n\notin M$ in specified type. We prove estimations is revision and a generalization for arithmetical progression earlier got result by V.A. Plaksin.
Keywords: Dirichlet character, Dirichlet $L$-function, exceptional set, representation numbers, exceptional zero, main member, remaining member.
Mots-clés : exceptional nature 
@article{IVM_2020_1_a1,
     author = {I. A. Allakov and A. Sh. Safarov},
     title = {On the exceptional set of the sum of a prime number and a fixed degree of a prime number},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--25},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_1_a1/}
}
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I. A. Allakov; A. Sh. Safarov. On the exceptional set of the sum of a prime number and a fixed degree of a prime number. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 11-25. http://geodesic.mathdoc.fr/item/IVM_2020_1_a1/