Landau's problems (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Landau's problems" in English language version.

refsWebsite

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19doi.org

2^nd place

18arxiv.org

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8worldcat.org

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6semanticscholar.org

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4harvard.edu

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2mtak.hu

low place

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2jstor.org

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2nih.gov

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1icm.edu.pl

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1ams.org

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1projecteuclid.org

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2,409^th place

1lynchburg.edu

low place

1ieee.org

652^nd place

515^th place

1stanford.edu

179^th place

183^rd place

1eudml.org

low place

ams.org

mathscinet.ams.org

D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12): 12. arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.

arxiv.org

Helfgott, H.A. (2013). "Major arcs for Goldbach's theorem". arXiv:1305.2897 [math.NT].
Helfgott, H.A. (2012). "Minor arcs for Goldbach's problem". arXiv:1205.5252 [math.NT].
Helfgott, H.A. (2013). "The ternary Goldbach conjecture is true". arXiv:1312.7748 [math.NT].
Bordignon, Matteo; Johnston, Daniel R.; Starichkova, Valeriia (2022). "An explicit version of Chen's theorem". arXiv:2207.09452 [math.NT].
Yamada, Tomohiro (2015-11-11). "Explicit Chen's theorem". arXiv:1511.03409 [math.NT].
Bordignon, Matteo; Starichkova, Valeriia (2022). "An explicit version of Chen's theorem assuming the Generalized Riemann Hypothesis". arXiv:2211.08844 [math.NT].
Johnston, Daniel R.; Starichkova, Valeriia V. (2022). "Some explicit results on the sum of a prime and an almost prime". arXiv:2208.01229 [math.NT].
Pintz, Janos (2018). "A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem". arXiv:1804.09084 [math.NT].
Heath-Brown, D.R.; Puchta, J.-C. (2002). "Integers Represented as a Sum of Primes and Powers of Two". arXiv:math/0201299.
D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12): 12. arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.
James, Maynard (2013). "Small gaps between primes". arXiv:1311.4600 [math.NT].
Alan Goldston, Daniel; Motohashi, Yoichi; Pintz, János; Yalçın Yıldırım, Cem (2006). "Small Gaps between Primes Exist". Proceedings of the Japan Academy, Series A. 82 (4): 61–65. arXiv:math/0505300. doi:10.3792/pjaa.82.61. S2CID 18847478.
Järviniemi, Olli (2022). "On large differences between consecutive primes". arXiv:2212.10965 [math.NT].
Heath-Brown, Roger (October 2020). "The Differences Between Consecutive Primes, V". International Mathematics Research Notices. 2021 (22): 17514–17562. arXiv:1906.09555. doi:10.1093/imrn/rnz295.
https://arxiv.org/abs/2505.00493
Merikoski, Jori (2022). "Largest prime factor of $n^{2}+1$ ". Journal of the European Mathematical Society. 25 (4): 1253–1284. arXiv:1908.08816. doi:10.4171/jems/1216. ISSN 1435-9855.
de la Bretèche, Régis; Drappeau, Sary (2020). "Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables". Journal of the European Mathematical Society. 22 (5): 1577–1624. arXiv:1703.03197. doi:10.4171/jems/951. ISSN 1435-9855. S2CID 146808221.
Baier, Stephan; Zhao, Liangyi (2006). "Bombieri–Vinogradov type theorems for sparse sets of moduli". Acta Arithmetica. 125 (2): 187–201. arXiv:math/0602116. Bibcode:2006AcAri.125..187B. doi:10.4064/aa125-2-5. ISSN 0065-1036.

doi.org

Vinogradow, I. M. (November 2002). "Representation of an odd number as a sum of three primes". The Goldbach Conjecture. Series in Pure Mathematics. Vol. 4. World Scientific. pp. 61–64. doi:10.1142/9789812776600_0003. ISBN 978-981-238-159-0.
Montgomery, H. L.; Vaughan, R. C. (1975). "The exceptional set in Goldbach's problem" (PDF). Acta Arithmetica. 27: 353–370. doi:10.4064/aa-27-1-353-370.
Pintz, J.; Ruzsa, I. Z. (July 2020). "On Linnik's approximation to Goldbach's problem. II" (PDF). Acta Mathematica Hungarica. 161 (2): 569–582. doi:10.1007/s10474-020-01077-8. S2CID 225457520.
Zhang, Yitang (May 2014). "Bounded gaps between primes". Annals of Mathematics. 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. ISSN 0003-486X.
D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12): 12. arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.
Alan Goldston, Daniel; Motohashi, Yoichi; Pintz, János; Yalçın Yıldırım, Cem (2006). "Small Gaps between Primes Exist". Proceedings of the Japan Academy, Series A. 82 (4): 61–65. arXiv:math/0505300. doi:10.3792/pjaa.82.61. S2CID 18847478.
Heath-Brown, Roger (October 2020). "The Differences Between Consecutive Primes, V". International Mathematics Research Notices. 2021 (22): 17514–17562. arXiv:1906.09555. doi:10.1093/imrn/rnz295.
Matomaki, K. (2007). "Large differences between consecutive primes". The Quarterly Journal of Mathematics. 58 (4): 489–518. doi:10.1093/qmath/ham021. ISSN 0033-5606..
Ingham, A. E. (1937). "On the difference between consecutive primes". Quarterly Journal of Mathematics. 8 (1): 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255.
Iwaniec, Henryk (1978). "Almost-primes represented by quadratic polynomials". Inventiones Mathematicae. 47 (2): 171–188. Bibcode:1978InMat..47..171I. doi:10.1007/BF01578070. ISSN 0020-9910. S2CID 122656097.
Lemke Oliver, Robert J. (2012). "Almost-primes represented by quadratic polynomials" (PDF). Acta Arithmetica. 151 (3): 241–261. doi:10.4064/aa151-3-2. ISSN 0065-1036.
Ankeny, N. C. (October 1952). "Representations of Primes by Quadratic Forms". American Journal of Mathematics. 74 (4): 913–919. doi:10.2307/2372233. JSTOR 2372233.
Harman, G.; Lewis, P. (2001). "Gaussian primes in narrow sectors". Mathematika. 48 (1–2): 119–135. doi:10.1112/S0025579300014388. S2CID 119730332.
Merikoski, Jori (2022). "Largest prime factor of $n^{2}+1$ ". Journal of the European Mathematical Society. 25 (4): 1253–1284. arXiv:1908.08816. doi:10.4171/jems/1216. ISSN 1435-9855.
de la Bretèche, Régis; Drappeau, Sary (2020). "Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables". Journal of the European Mathematical Society. 22 (5): 1577–1624. arXiv:1703.03197. doi:10.4171/jems/951. ISSN 1435-9855. S2CID 146808221.
Hooley, Christopher (July 1967). "On the greatest prime factor of a quadratic polynomial". Acta Mathematica. 117: 281–299. doi:10.1007/BF02395047.
Todd, John (1949). "A Problem on Arc Tangent Relations". The American Mathematical Monthly. 56 (8): 517–528. doi:10.2307/2305526. JSTOR 2305526.
Friedlander, John; Iwaniec, Henryk (1997). "Using a parity-sensitive sieve to count prime values of a polynomial". Proceedings of the National Academy of Sciences. 94 (4): 1054–1058. Bibcode:1997PNAS...94.1054F. doi:10.1073/pnas.94.4.1054. ISSN 0027-8424. PMC 19742. PMID 11038598..
Baier, Stephan; Zhao, Liangyi (2006). "Bombieri–Vinogradov type theorems for sparse sets of moduli". Acta Arithmetica. 125 (2): 187–201. arXiv:math/0602116. Bibcode:2006AcAri.125..187B. doi:10.4064/aa125-2-5. ISSN 0065-1036.

eudml.org

Jean-Marc Deshouillers and Henryk Iwaniec, On the greatest prime factor of $n^{2}+1$ , Annales de l'Institut Fourier 32:4 (1982), pp. 1–11.

harvard.edu

ui.adsabs.harvard.edu

Ingham, A. E. (1937). "On the difference between consecutive primes". Quarterly Journal of Mathematics. 8 (1): 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255.
Iwaniec, Henryk (1978). "Almost-primes represented by quadratic polynomials". Inventiones Mathematicae. 47 (2): 171–188. Bibcode:1978InMat..47..171I. doi:10.1007/BF01578070. ISSN 0020-9910. S2CID 122656097.
Friedlander, John; Iwaniec, Henryk (1997). "Using a parity-sensitive sieve to count prime values of a polynomial". Proceedings of the National Academy of Sciences. 94 (4): 1054–1058. Bibcode:1997PNAS...94.1054F. doi:10.1073/pnas.94.4.1054. ISSN 0027-8424. PMC 19742. PMID 11038598..
Baier, Stephan; Zhao, Liangyi (2006). "Bombieri–Vinogradov type theorems for sparse sets of moduli". Acta Arithmetica. 125 (2): 187–201. arXiv:math/0602116. Bibcode:2006AcAri.125..187B. doi:10.4064/aa125-2-5. ISSN 0065-1036.

icm.edu.pl

matwbn.icm.edu.pl

Montgomery, H. L.; Vaughan, R. C. (1975). "The exceptional set in Goldbach's problem" (PDF). Acta Arithmetica. 27: 353–370. doi:10.4064/aa-27-1-353-370.

ieee.org

ieeexplore.ieee.org

Heath-Brown, Roger (October 2020). "The Differences Between Consecutive Primes, V". International Mathematics Research Notices. 2021 (22): 17514–17562. arXiv:1906.09555. doi:10.1093/imrn/rnz295.

jstor.org

Ankeny, N. C. (October 1952). "Representations of Primes by Quadratic Forms". American Journal of Mathematics. 74 (4): 913–919. doi:10.2307/2372233. JSTOR 2372233.
Todd, John (1949). "A Problem on Arc Tangent Relations". The American Mathematical Monthly. 56 (8): 517–528. doi:10.2307/2305526. JSTOR 2305526.

lynchburg.edu

faculty.lynchburg.edu

Nicely, Thomas R. "First occurrence prime gaps". University of Lynchburg. Retrieved 2024-09-11.

mtak.hu

real.mtak.hu

Pintz, János. "An Approximate Formula for Goldbach's Problem with Applications" (PDF). mtak.hu.
Pintz, J.; Ruzsa, I. Z. (July 2020). "On Linnik's approximation to Goldbach's problem. II" (PDF). Acta Mathematica Hungarica. 161 (2): 569–582. doi:10.1007/s10474-020-01077-8. S2CID 225457520.

nih.gov

ncbi.nlm.nih.gov

Friedlander, John; Iwaniec, Henryk (1997). "Using a parity-sensitive sieve to count prime values of a polynomial". Proceedings of the National Academy of Sciences. 94 (4): 1054–1058. Bibcode:1997PNAS...94.1054F. doi:10.1073/pnas.94.4.1054. ISSN 0027-8424. PMC 19742. PMID 11038598..

pubmed.ncbi.nlm.nih.gov

Friedlander, John; Iwaniec, Henryk (1997). "Using a parity-sensitive sieve to count prime values of a polynomial". Proceedings of the National Academy of Sciences. 94 (4): 1054–1058. Bibcode:1997PNAS...94.1054F. doi:10.1073/pnas.94.4.1054. ISSN 0027-8424. PMC 19742. PMID 11038598..

projecteuclid.org

Alan Goldston, Daniel; Motohashi, Yoichi; Pintz, János; Yalçın Yıldırım, Cem (2006). "Small Gaps between Primes Exist". Proceedings of the Japan Academy, Series A. 82 (4): 61–65. arXiv:math/0505300. doi:10.3792/pjaa.82.61. S2CID 18847478.

semanticscholar.org

api.semanticscholar.org

Pintz, J.; Ruzsa, I. Z. (July 2020). "On Linnik's approximation to Goldbach's problem. II" (PDF). Acta Mathematica Hungarica. 161 (2): 569–582. doi:10.1007/s10474-020-01077-8. S2CID 225457520.
D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12): 12. arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.
Alan Goldston, Daniel; Motohashi, Yoichi; Pintz, János; Yalçın Yıldırım, Cem (2006). "Small Gaps between Primes Exist". Proceedings of the Japan Academy, Series A. 82 (4): 61–65. arXiv:math/0505300. doi:10.3792/pjaa.82.61. S2CID 18847478.
Iwaniec, Henryk (1978). "Almost-primes represented by quadratic polynomials". Inventiones Mathematicae. 47 (2): 171–188. Bibcode:1978InMat..47..171I. doi:10.1007/BF01578070. ISSN 0020-9910. S2CID 122656097.
Harman, G.; Lewis, P. (2001). "Gaussian primes in narrow sectors". Mathematika. 48 (1–2): 119–135. doi:10.1112/S0025579300014388. S2CID 119730332.
de la Bretèche, Régis; Drappeau, Sary (2020). "Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables". Journal of the European Mathematical Society. 22 (5): 1577–1624. arXiv:1703.03197. doi:10.4171/jems/951. ISSN 1435-9855. S2CID 146808221.

stanford.edu

Lemke Oliver, Robert J. (2012). "Almost-primes represented by quadratic polynomials" (PDF). Acta Arithmetica. 151 (3): 241–261. doi:10.4064/aa151-3-2. ISSN 0065-1036.

worldcat.org

search.worldcat.org

Zhang, Yitang (May 2014). "Bounded gaps between primes". Annals of Mathematics. 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. ISSN 0003-486X.
Matomaki, K. (2007). "Large differences between consecutive primes". The Quarterly Journal of Mathematics. 58 (4): 489–518. doi:10.1093/qmath/ham021. ISSN 0033-5606..
Iwaniec, Henryk (1978). "Almost-primes represented by quadratic polynomials". Inventiones Mathematicae. 47 (2): 171–188. Bibcode:1978InMat..47..171I. doi:10.1007/BF01578070. ISSN 0020-9910. S2CID 122656097.
Lemke Oliver, Robert J. (2012). "Almost-primes represented by quadratic polynomials" (PDF). Acta Arithmetica. 151 (3): 241–261. doi:10.4064/aa151-3-2. ISSN 0065-1036.
Merikoski, Jori (2022). "Largest prime factor of $n^{2}+1$ ". Journal of the European Mathematical Society. 25 (4): 1253–1284. arXiv:1908.08816. doi:10.4171/jems/1216. ISSN 1435-9855.
de la Bretèche, Régis; Drappeau, Sary (2020). "Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables". Journal of the European Mathematical Society. 22 (5): 1577–1624. arXiv:1703.03197. doi:10.4171/jems/951. ISSN 1435-9855. S2CID 146808221.
Friedlander, John; Iwaniec, Henryk (1997). "Using a parity-sensitive sieve to count prime values of a polynomial". Proceedings of the National Academy of Sciences. 94 (4): 1054–1058. Bibcode:1997PNAS...94.1054F. doi:10.1073/pnas.94.4.1054. ISSN 0027-8424. PMC 19742. PMID 11038598..
Baier, Stephan; Zhao, Liangyi (2006). "Bombieri–Vinogradov type theorems for sparse sets of moduli". Acta Arithmetica. 125 (2): 187–201. arXiv:math/0602116. Bibcode:2006AcAri.125..187B. doi:10.4064/aa125-2-5. ISSN 0065-1036.