On the Exceptional Set of the Sum of a Prime Number and a Fixed Degree of a Prime Number

被引：0

作者：

I. Allakov

A. Sh. Safarov

机构：

[1] Termez State University,

来源：

Russian Mathematics | 2020年 / 64卷

关键词：

Dirichlet character; Dirichlet L-function; exceptional set; number representation; exceptional zero; exceptional real character; main member; remaining member;

D O I：

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学科分类号：

摘要：

Let X be a sufficiently great real number and M denote the set of natural numbers not exceeding X which cannot be written as a sum of a prime and a fixed degree of a prime number from the arithmetical progression with difference d. Let Ed(X) = cardM. We obtain a new numerical degree estimate for the set Ed(X) and an estimate from below for the number of presentations of n ∉ M in the specified type. The proven estimates refine the generalization for an arithmetical progression of results earlier got by V.A. Plaksin.

引用

页码：8 / 21

页数：13

共 9 条

[1] Plaksin VA(1990)On a Problem of Hua Loo Keng Math. Notes 47 278-286
[2] Montgomery HL(1975)The Exceptional Set in Goldbach’s Problem Acta Arith. 27 353-370
[3] Vaughan RC(1985)The Binary Hardy-Littlewood Problem Acta Arith. 46 33-56
[4] Vinogradov AI(1989)A New Iterative Method in Warings Problems Acta Math. 162 1-71
[5] Vaughan RC(1987)Generalization of a Theorem of Gallagher for the Primes of an Arithmetic Progression Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk 1 13-18
[6] Allakov IA(1970)A large sieve density estimate near σ =1 Invent. Math. 11 329-339
[7] Khamzaev E(1990)An Estimate for Trigonometric Sums in Powers of Prime Numbers in an Arithmetic Progression Dokl. Akad. Nauk UzSSR 9 3-4
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