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Lower bounds for simultaneous Diophantine approximation constants
Communications in Mathematics, Tome 22 (2014) no. 1, pp. 71-76 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $\theta _s$, new lower bounds are deduced for $\theta _6$ and $\theta _7$.
After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $\theta _s$, new lower bounds are deduced for $\theta _6$ and $\theta _7$.
Classification : 11H16, 11J13
Keywords: geometry of numbers; Diophantine approximation; approximation constants; critical determinant 
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Nowak, Werner Georg. Lower bounds for simultaneous Diophantine approximation constants. Communications in Mathematics, Tome 22 (2014) no. 1, pp. 71-76. http://geodesic.mathdoc.fr/item/COMIM_2014_22_1_a5/

[1] Armitage, J.V.: On a method of Mordell in the geometry of numbers. Mathematika, 2, 1955, 132-140, | DOI | MR | Zbl

[2] Blichfeldt, H.: A new principle in the geometry of numbers, with some applications. Trans. Amer. Math. Soc., 15, 1914, 227-235, | DOI | MR

[3] Davenport, H.: On the product of three homogeneous linear forms. J. London Math. Soc., 13, 1938, 139-145, | DOI | MR | Zbl

[4] Davenport, H.: On the minimum of a ternary cubic form. J. London Math. Soc., 19, 1944, 13-18, | DOI | MR | Zbl

[5] Davenport, H.: On a theorem of Furtwängler. J. London Math. Soc., 30, 1955, 185-195, | MR | Zbl

[6] Davenport, H., Mahler, K.: Simultaneous Diophantine approximation. Duke Math. J., 13, 1946, 105-111, | DOI | MR | Zbl

[7] Gruber, P.M., Lekkerkerker, C.G.: Geometry of numbers. 1987, North Holland, Amsterdam, | MR | Zbl

[8] Mordell, L.J.: The product of three homogeneous linear ternary forms. J. London Math. Soc., 17, 1942, 107-115, | DOI | MR | Zbl

[9] Mordell, L.J.: Observation on the minimum of a positive quadratic form in eight variables. J. London Math. Soc., 19, 1944, 3-6, | DOI | MR | Zbl

[10] Mordell, L.J.: On the minimum of a ternary cubic form. J. London Math. Soc., 19, 1944, 6-12, | DOI | MR | Zbl

[11] Niven, I., Zuckerman, H.S.: Einführung in die Zahlentheorie. 1975, Bibliograph. Inst., Mannheim,

[12] Nowak, W.G.: On simultaneous Diophantine approximation. Rend. Circ. Mat. Palermo, Ser. II, 33, 1984, 456-460, | MR | Zbl

[13] Nowak, W.G.: The critical determinant of the double paraboloid and Diophantine approximation in ${\fam 5 R}^3$ and ${\fam 5 R}^4$. Math. Pannonica, 10, 1999, 111-122, | MR

[14] Nowak, W.G.: Diophantine approximation in ${\fam 5 R}^s$: On a method of Mordell and Armitage. Algebraic number theory and Diophantine analysis. Proceedings of the conference held in Graz, Austria, August 30 to September 5, 1998, 2000, 339-349, W. de Gruyter, Berlin, | MR

[15] Prasad, A.V.: Simultaneous Diophantine approximation. Proc. Indian Acad. Sci. A, 31, 1950, 1-15, | MR | Zbl

[16] Spohn, W.G.: Blichfeldt's theorem and simultaneous Diophantine approximation. Amer. J. Math., 90, 1968, 885-894, | DOI | MR

[17] Žilinskas, G.: On the product of four homogeneous linear forms. J. London Math. Soc., 16, 1941, 27-37, | DOI | MR | Zbl