Sur des équations diophantiennes généralisant celle de Markoff

Serge Perrine

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

• Volume: 6, Issue: 1, page 127-141
• ISSN: 0240-2963

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Perrine, Serge. "Sur des équations diophantiennes généralisant celle de Markoff." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.1 (1997): 127-141. <http://eudml.org/doc/73410>.

@article{Perrine1997,
author = {Perrine, Serge},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Markoff equations; cubic diophantine equations},
language = {fre},
number = {1},
pages = {127-141},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Sur des équations diophantiennes généralisant celle de Markoff},
url = {http://eudml.org/doc/73410},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Perrine, Serge
TI - Sur des équations diophantiennes généralisant celle de Markoff
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 1
SP - 127
EP - 141
LA - fre
KW - Markoff equations; cubic diophantine equations
UR - http://eudml.org/doc/73410
ER -

References

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3. [3] Mordell ( L.J.) .— Diophantine equations, Academic PressNew-York (1969). Zbl0188.34503MR249355
4. [4] Hurwitz ( A.) .— Uber eine Aufgabe der unbestimmten Analysis, Archiv. der Math. und Phys.3, n° 14 (1907), pp. 185-196. JFM38.0246.01
5. [5] Schwartz et Muhly ( H.T.) . — On a class of cubic diophantine equations, J. Lond. Math. Soc.32 (1957), pp. 379-383. Zbl0080.26001MR91292
6. [6] Mills ( W.H.) . — Certain diophantine equations linear in one unknown, Canad. J. Math.8 (1956), pp. 5-12. Zbl0070.27202MR75222
7. [7] Pollington ( A.D.) et Moran ( W.) .— Number Theory with an emphasis on the Markoff spectrum, M. DekkerNew-York (1993). Zbl0778.00034MR1219317
8. [8] Perrine ( S.) . — Approximation diophantienne (théorie de Markoff), Thèse présentée à l'Université de Metz (décembre 1988). 
9. [9] Silverman ( J.H.) .— The Markoff equation X2 + Y2 + Z2 = aXYZ over quadratic imaginary fields, J. Number Theory35, tome 1 (1990), pp. 72-104. Zbl0702.11012MR1054560
10. [10] Manin ( Y.) et Tsfasman ( M.A.) .- Rational varieties : algebra, geometry and arithmetic, Uspekhi Mat. Nauk41, n° 2 (1986), pp. 43-94; Russian math. surveys41 (1986) pp. 51-116. Zbl0621.14029MR842161
11. [11] Perrine ( S.) .— Sur une généralisation de la théorie de Markoff, J. Number Theory37 (1991), pp. 211-230. Zbl0714.11039MR1092607
12. [12] Cusick ( T.W.) .— On Perrine's generalized Markoff equations, Aequationes Mathematicae46, n° 3 (1993), pp. 203-211. Zbl0813.11013MR1232042
13. [13] Frobenius ( G.) .— Uber die Markoffschen Zahlen, Preussiche Akad. Wiss. SB (1913), pp. 458-487. Zbl44.0255.01JFM44.0255.01
14. [14] Grosswald ( E.) .— Representations of integers as sums of squares, Springer Verlag, New-York - Berlin (1985). Zbl0574.10045MR803155
15. [15] Herzberg ( W.) .— On a problem of Hurwitz, Pacific J. Math.50 (1974), pp. 485-493. Zbl0247.10010MR347731
16. [16] Cohn ( H.) .— Representation of Markoff's binary quadratic forms by geodesics on a perforated torus, Acta ArithmeticaXVII (1971), pp. 123-136. Zbl0218.10041MR288079
17. [17] EL KHUTI EL'HUTI ( M. Kh.) .— Cubic surfaces of Markov type, Mat. Sb93 (1974), pp. 331-336; Math USSR-Sb22 (1974), pp. 333-348. Zbl0303.14005
18. [18] Baragar ( A.) .— Integral Solutions of Markoff Hurwitz equations, J. Number Theory49 (1994), pp. 27-44. Zbl0820.11016MR1295950

Citations in EuDML Documents

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1. Serge Perrine, Un arbre de constantes d'approximation analogue à celui de l'équation diophantienne de Markoff

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