In 1985, Yu. V. Nesterenko produced a criterion for linear independence,which is a variant of Siegel's. While Siegel uses upper bounds on full systemsof forms, Nesterenko uses upper and lower bounds on sufficiently densesequences of individual forms. The proof of Nesterenko's criterion wassimplified by F. Amoroso and P. Colmez in 2003. More recently, S. Fischler andW. Zudilin produced a refinement, together with a much simpler proof. This newproof rests on a simple argument which we expand here. We get a new result,which contains Nesterenko's criterion, as well as criteria for algebraicindependence.
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机译：1985年，于。 V. Nesterenko提出了线性独立性的标准，这是Siegel的变体。 Siegel在整个形式系统中使用上限，而Nesterenko在单个形式的足够密集的序列上使用上限和下限。 F. Amoroso和P. Colmez在2003年简化了Nesterenko标准的证明。最近，S。Fischler和W. Zudilin进行了改进，并提供了更为简单的证明。这个新证明基于一个简单的论点，我们在这里进行扩展。我们得到一个新的结果，其中包含Nesterenko的准则以及代数独立性的准则。
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