On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus

Karin Halupczok[1]

  • [1] Albert-Ludwigs-Universität Freiburg Eckerstr. 1 D-79104 Freiburg, Allemagne

Journal de Théorie des Nombres de Bordeaux (2009)

  • Volume: 21, Issue: 1, page 203-213
  • ISSN: 1246-7405

Abstract

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For ε > 0 and any sufficiently large odd n we show that for almost all k ≤ R : = n 1 / 5 - ε there exists a representation n = p 1 + p 2 + p 3 with primes p i ≡ b i mod k for almost all admissible triplets b 1 , b 2 , b 3 of reduced residues mod k .

How to cite

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Halupczok, Karin. "On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus." Journal de Théorie des Nombres de Bordeaux 21.1 (2009): 203-213. <http://eudml.org/doc/10872>.

@article{Halupczok2009,
abstract = {For $\varepsilon &gt;0$ and any sufficiently large odd $n$ we show that for almost all $k\le R:=n^\{1/5-\varepsilon \}$ there exists a representation $n=p_\{1\}+p_\{2\}+p_\{3\}$ with primes $p_\{i\}\equiv b_\{i\}$ mod $k$ for almost all admissible triplets $b_\{1\},b_\{2\},b_\{3\}$ of reduced residues mod $k$.},
affiliation = {Albert-Ludwigs-Universität Freiburg Eckerstr. 1 D-79104 Freiburg, Allemagne},
author = {Halupczok, Karin},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {ternary Goldbach problem; primes in progression},
language = {eng},
number = {1},
pages = {203-213},
publisher = {Université Bordeaux 1},
title = {On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus},
url = {http://eudml.org/doc/10872},
volume = {21},
year = {2009},
}

TY - JOUR
AU - Halupczok, Karin
TI - On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2009
PB - Université Bordeaux 1
VL - 21
IS - 1
SP - 203
EP - 213
AB - For $\varepsilon &gt;0$ and any sufficiently large odd $n$ we show that for almost all $k\le R:=n^{1/5-\varepsilon }$ there exists a representation $n=p_{1}+p_{2}+p_{3}$ with primes $p_{i}\equiv b_{i}$ mod $k$ for almost all admissible triplets $b_{1},b_{2},b_{3}$ of reduced residues mod $k$.
LA - eng
KW - ternary Goldbach problem; primes in progression
UR - http://eudml.org/doc/10872
ER -

References

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  1. A. Balog, The Prime k -Tuplets Conjecture on Average. Analytic number theory, Proc. Conf. in Honor of Paul T. Bateman, Urbana/IL (USA), 1989, Prog. Math. 85 (1990), 47–75. Zbl0719.11066MR1084173
  2. C. Bauer, Y. Wang, On the Goldbach conjecture in arithmetic progressions. Rocky Mountain J. Math. 36 (1) (2006), 35–66. Zbl1148.11053MR2228183
  3. Z. Cui, The ternary Goldbach problem in arithmetic progression II. Acta Math. Sinica (Chin. Ser.) 49 (1) (2006), 129–138. Zbl1230.11122MR2248920
  4. J. Liu, T. Zhang, The ternary Goldbach problem in arithmetic progressions. Acta Arith. 82 (3) (1997), 197–227. Zbl0889.11035MR1482887
  5. M. B. Nathanson, Additive Number Theory: The Classical Bases. Graduate texts in Mathematics 164, Springer-Verlag, 1996. Zbl0859.11002MR1395371

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