Abstract
Siegel’s Lemma in its original form guarantees the existence of a small non-trivial integral solution of a system of linear equations with rational integer coefficients and with more variables than equations. It reads as follows: 1 Lemma. (C.L. Siegel) Let A = (a ij ) be an N × M matrix with rational integer coefficients. Put a = max i,j |a ij |. Tien, if N < M, the equation Ax = 0 has a solution x ∈ ℤM, x≠0, with
where ‖ ‖ denotes the max-norm: ‖x‖=‖(x1,...,x M ‖=max1≤i≤M|x i | in ℝM.
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© 1993 Springer-Verlag Berlin Heidelberg
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Kooman, RJ. (1993). Faltings’s Version of Siegel’s Lemma. In: Edixhoven, B., Evertse, JH. (eds) Diophantine Approximation and Abelian Varieties. Lecture Notes in Mathematics, vol 1566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48208-6_10
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DOI: https://doi.org/10.1007/978-3-540-48208-6_10
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