M. Bôcher, Amer The theory of linear dependence Certain cases in which the vanishing of the Wronskian is a sufficient condition for linear dependence, Math. Soc. Ann. of Math. Trans. Amer. Math. Soc, vol.7, issue.2, pp.120-121, 1900.

J. W. Cassels, An Introduction to Diophantine Approximation, Cambridge Tracts in Mathematics and Mathematical Physics, issue.45, 1957.

D. R. Curtiss, The vanishing of the wronskian and the problem of linear dependence, Mathematische Annalen, vol.65, issue.2, pp.282-298, 1908.
DOI : 10.1007/BF01450000

F. J. Dyson, The approximation to algebraic numbers by rationals, Acta Mathematica, vol.79, issue.0, pp.225-240, 1947.
DOI : 10.1007/BF02404697

G. Frobenius, Ueber die Determinante mehrerer Functionen einer Variabeln, J. Reine Angew. Math, vol.77, pp.245-257, 1874.
DOI : 10.1007/978-3-642-49211-2_6

W. Hurewicz, Lectures on Ordinary Differential Equations, Technology Press of the Massachusetts Institute of Technology, 1958.

I. Kaplansky, An Introduction to Differential Algebra, 1976.

A. V. Kiselev, Associative homotopy Lie algebras and Wronskians, Journal of Mathematical Sciences, vol.219, issue.4, pp.1016-1030, 2007.
DOI : 10.1007/s10958-007-0028-2

M. Krusemeyer, Why Does the Wronskian Work?, The American Mathematical Monthly, vol.95, issue.1, pp.46-49, 1988.
DOI : 10.2307/2323448

W. J. Leveque, Topics in Number Theory, 2002.

A. R. Magid, Lectures on Differential Galois Theory, 1994.
DOI : 10.1090/ulect/007

K. Mahler, Lectures on Diophantine Approximations. Part I: g-adic Numbers and Roth's Theorem, 1961.

S. J. Miller and R. Takloo-bighash, An Invitation to Modern Number Theory, 2006.

D. J. Newman and M. L. Slater, Waring's problem for the ring of polynomials, Journal of Number Theory, vol.11, issue.4, pp.477-487, 1979.
DOI : 10.1016/0022-314X(79)90027-1

A. Ostrowski, ???ber ein Analogon der Wronskischen Determinante bei Funktionen mehrerer Ver???nderlicher, Uber ein Analogon der Wronskischen Determinante bei Funktionen mehrerer Veränderlicher, pp.223-230, 1919.
DOI : 10.1007/BF01203013

E. G. Poole, Introduction to the Theory of Linear Differential Equations, 1960.

K. F. Roth, RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS, Mathematika, vol.2, pp.1-20, 1955.
DOI : 10.1142/9789812385215_0009

W. M. Schmidt, Diophantine approximation, Lecture Notes in Mathematics, vol.785, 1980.
DOI : 10.1007/BFb0098248
URL : https://hal.archives-ouvertes.fr/hal-01299504

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