# Goldbach’s problem with primes in arithmetic progressions and in short intervals

Karin Halupczok^{[1]}

- [1] Universität Münster Mathematisches Institut Einsteinstr. 62 D-48149 Münster, Germany

Journal de Théorie des Nombres de Bordeaux (2013)

- Volume: 25, Issue: 2, page 331-351
- ISSN: 1246-7405

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topHalupczok, Karin. "Goldbach’s problem with primes in arithmetic progressions and in short intervals." Journal de Théorie des Nombres de Bordeaux 25.2 (2013): 331-351. <http://eudml.org/doc/275735>.

@article{Halupczok2013,

abstract = {Some mean value theorems in the style of Bombieri-Vinogradov’s theorem are discussed. They concern binary and ternary additive problems with primes in arithmetic progressions and short intervals. Nontrivial estimates for some of these mean values are given. As application inter alia, we show that for large odd $n\lnot \equiv 1\:(6)$, Goldbach’s ternary problem $n=p_1+p_2+p_3$ is solvable with primes $p_\{1\},p_\{2\}$ in short intervals $p_i \in [X_i,X_i+Y]$ with $X_\{i\}^\{\theta _\{i\}\}=Y$, $i=1,2$, and $\theta _\{1\},\theta _\{2\}\ge 0.933$ such that $(p_\{1\}+2)(p_\{2\}+2)$ has at most $9$ prime factors.},

affiliation = {Universität Münster Mathematisches Institut Einsteinstr. 62 D-48149 Münster, Germany},

author = {Halupczok, Karin},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {additive problems; circle method; sieve methods; short intervals; short interval},

language = {eng},

month = {9},

number = {2},

pages = {331-351},

publisher = {Société Arithmétique de Bordeaux},

title = {Goldbach’s problem with primes in arithmetic progressions and in short intervals},

url = {http://eudml.org/doc/275735},

volume = {25},

year = {2013},

}

TY - JOUR

AU - Halupczok, Karin

TI - Goldbach’s problem with primes in arithmetic progressions and in short intervals

JO - Journal de Théorie des Nombres de Bordeaux

DA - 2013/9//

PB - Société Arithmétique de Bordeaux

VL - 25

IS - 2

SP - 331

EP - 351

AB - Some mean value theorems in the style of Bombieri-Vinogradov’s theorem are discussed. They concern binary and ternary additive problems with primes in arithmetic progressions and short intervals. Nontrivial estimates for some of these mean values are given. As application inter alia, we show that for large odd $n\lnot \equiv 1\:(6)$, Goldbach’s ternary problem $n=p_1+p_2+p_3$ is solvable with primes $p_{1},p_{2}$ in short intervals $p_i \in [X_i,X_i+Y]$ with $X_{i}^{\theta _{i}}=Y$, $i=1,2$, and $\theta _{1},\theta _{2}\ge 0.933$ such that $(p_{1}+2)(p_{2}+2)$ has at most $9$ prime factors.

LA - eng

KW - additive problems; circle method; sieve methods; short intervals; short interval

UR - http://eudml.org/doc/275735

ER -

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