Advanced search
Publication Cover
Experimental Mathematics Volume 31, 2022 - Issue 1
Submit an article Journal homepage
142
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Refined Goldbach Conjectures with Primes in Progressions

Kimball MartinDepartment of Mathematics, University of Oklahoma, Norman, OK, USACorrespondence[email protected]
View further author information
Pages 226-232 | Published online: 14 Apr 2019

References

  • [Ayoub 53] R. Ayoub. “On Rademacher's Extension of the Goldbach-Vinogradoff Theorem.” Trans. Amer. Math. Soc. 74 (1953), 482–91.
  • [Bauer 01] C. Bauer. “On Goldbach's Conjecture in Arithmetic Progressions.” Studia Sci. Math. Hungar. 37:1–2 (2001), 1–20.
  • [Bauer 17] C. Bauer. “Goldbach's Conjecture in Arithmetic Progressions: Number and Size of Exceptional Prime Moduli.” Arch. Math. 108:2 (2017), 159–72.
  • [Bauer and Wang 13] C. Bauer, and Y. Wang. “The Binary Goldbach Conjecture with Primes in Arithmetic Progressions with Large Modulus.” Acta Arith. 159:3 (2013), 227–43.
  • [Bhowmik et al. 19] G. Bhowmik, K. Halupczok, K. Matsumoto, and Y. Suzuki. “Goldbach Representations in Arithmetic Progressions and zeros of Dirichlet L-functions.” Mathematika. 65:1 (2019), 57–97.
  • [Chowla 34] S. Chowla. “On the Least Prime in an Arithmetical Progression.” J. Indian Math. Soc., New Ser. 1 (1934), 1–3.
  • [Granville 07] A. Granville. “Refinements of Goldbach's Conjecture, and the Generalized Riemann hypothesis.” Funct. Approx. Comment. Math. 37:1 (2007), 159–73.
  • [Helfgott 13] H. A. Helfgott. The Ternary Goldbach Conjecture Is True. (2013) preprint, available at https://arxiv.org/abs/1312.7748.
  • [Lavrik 61] A. F. Lavrik. “The Number of k-Twin Primes Lying on an Interval of a Given Length.” Soviet Math. Dokl. 2 (1961), 52–5.
  • [Li and Pan 10] H. Li, and H. Pan. “A Density Version of Vinogradov's Three Primes Theorem.” Forum Math. 22:4 (2010), 699–714.
  • [Liu and Zhan 97] M.-C. Liu, and T. Zhan. “The Goldbach Problem with Primes in Arithmetic Progressions.” In Analytic Number Theory (Kyoto, 1996), London Math. Soc. Lecture Note Ser. vol. 247, pp. 227–51. Cambridge: Cambridge Univ. Press, 1997.
  • [Oliveira e Silva et al. 14] T. Oliveira e Silva, S. Herzog, and S. Pardi. “Empirical veri_cation of the Even Goldbach Conjecture and Computation of Prime Gaps up to 4·1018.” Math. Comp. 83:288 (2014), 2033–60.
  • [Rademacher 26] H. Rademacher. “Über eine Erweiterung des Goldbachschen Problems.” Math. Z. 25:1 (1926), 627–57. DOI https://doi.org/10.1007/BF01283858 (German). MR1544830
  • [Shao 14] X. Shao. “A Density Version of the Vinogradov Three Primes Theorem.” Duke Math. J. 163:3 (2014), 489–512.
  • [Shen 16] Q. Shen. “The Ternary Goldbach Problem with Primes in Positive Density Sets.” J. Number Theory. 168 (2016), 334–45.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.