Diophantine approximation (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Diophantine approximation" in English language version.

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Hurwitz 1891, p. 279 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Hurwitz 1891, p. 284 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Hardy & Wright 1979, Chapter 10.11 Hardy, G. H.; Wright, E. M. (1979). An Introduction to the Theory of Numbers (5th ed.). Oxford University Press. ISBN 978-0-19-853170-8. MR 0568909.
Hardy & Wright 1979, p. 164 Hardy, G. H.; Wright, E. M. (1979). An Introduction to the Theory of Numbers (5th ed.). Oxford University Press. ISBN 978-0-19-853170-8. MR 0568909.
Hurwitz 1891 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Bernik et al. 2013, p. 24 Bernik, V.; Beresnevich, V.; Götze, F.; Kukso, O. (2013). "Distribution of algebraic numbers and metric theory of Diophantine approximation". In Eichelsbacher, Peter; Elsner, Guido; Kösters, Holger; Löwe, Matthias; Merkl, Franz; Rolles, Silke (eds.). Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Götze. Springer Proceedings in Mathematics & Statistics. Vol. 42. Heidelberg: Springer. pp. 23–48. doi:10.1007/978-3-642-36068-8_2. ISBN 978-3-642-36067-1. MR 3079136. S2CID 55652124.
Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419

archive.org

Perron 1913, Chapter 2, Theorem 15 Perron, Oskar (1913). Die Lehre von den Kettenbrüchen [The Theory of Continued Fractions] (in German). Leipzig: B. G. Teubner.

arxiv.org

Koukoulopoulos, D.; Maynard, J. (2019). "On the Duffin–Schaeffer conjecture". arXiv:1907.04593 [math.NT].

books.google.com

Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419

doi.org

Hurwitz 1891, p. 279 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Hurwitz 1891, p. 284 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Hurwitz 1891 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Bernik et al. 2013, p. 24 Bernik, V.; Beresnevich, V.; Götze, F.; Kukso, O. (2013). "Distribution of algebraic numbers and metric theory of Diophantine approximation". In Eichelsbacher, Peter; Elsner, Guido; Kösters, Holger; Löwe, Matthias; Merkl, Franz; Rolles, Silke (eds.). Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Götze. Springer Proceedings in Mathematics & Statistics. Vol. 42. Heidelberg: Springer. pp. 23–48. doi:10.1007/978-3-642-36068-8_2. ISBN 978-3-642-36067-1. MR 3079136. S2CID 55652124.
Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419

hathitrust.org

catalog.hathitrust.org

See Perron 1929, Chapter 2, Theorem 23, p. 63 Perron, Oskar (1929). Die Lehre von den Kettenbrüchen [The Theory of Continued Fractions] (in German) (2nd ed.). Chelsea.{{cite book}}: CS1 maint: location missing publisher (link)

jussieu.fr

math.jussieu.fr

See Michel Waldschmidt: Introduction to Diophantine methods irrationality and transcendence Archived 2012-02-09 at the Wayback Machine, pp 24–26.

scientificamerican.com

Sloman, Leila (2019). "New Proof Solves 80-Year-Old Irrational Number Problem". Scientific American.

semanticscholar.org

api.semanticscholar.org

Hurwitz 1891, p. 279 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Hurwitz 1891, p. 284 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Hurwitz 1891 Hurwitz, A. (1891). "Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche" [On the approximate representation of irrational numbers by rational fractions]. Mathematische Annalen (in German). 39 (2): 279–284. doi:10.1007/BF01206656. MR 1510702. S2CID 119535189.
Bernik et al. 2013, p. 24 Bernik, V.; Beresnevich, V.; Götze, F.; Kukso, O. (2013). "Distribution of algebraic numbers and metric theory of Diophantine approximation". In Eichelsbacher, Peter; Elsner, Guido; Kösters, Holger; Löwe, Matthias; Merkl, Franz; Rolles, Silke (eds.). Limit Theorems in Probability, Statistics and Number Theory: In Honor of Friedrich Götze. Springer Proceedings in Mathematics & Statistics. Vol. 42. Heidelberg: Springer. pp. 23–48. doi:10.1007/978-3-642-36068-8_2. ISBN 978-3-642-36067-1. MR 3079136. S2CID 55652124.

web.archive.org

See Michel Waldschmidt: Introduction to Diophantine methods irrationality and transcendence Archived 2012-02-09 at the Wayback Machine, pp 24–26.

zbmath.org

Lang 1995, p. 9 Lang, Serge (1995). Introduction to Diophantine Approximations (New expanded ed.). Springer-Verlag. ISBN 0-387-94456-7. Zbl 0826.11030.
Bugeaud 2012, p. 245 Bugeaud, Yann (2012). Distribution modulo one and Diophantine approximation. Cambridge Tracts in Mathematics. Vol. 193. Cambridge: Cambridge University Press. ISBN 978-0-521-11169-0. Zbl 1260.11001.