Geodesic
Geometry of Diophantine exponents
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 2, pp. 273-347

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Diophantine exponents are some of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of Diophantine approximation that studies Diophantine exponents and relations they satisfy. We discuss classical Diophantine exponents arising in the problem of approximating zero with the set of the values of several linear forms at integer points, their analogues in Diophantine approximation with weights, multiplicative Diophantine exponents, and Diophantine exponents of lattices. We pay special attention to the transference principle. Bibliography: 99 titles.
Keywords: geometry of numbers, Diophantine exponents, transference principle.
Mots-clés : Diophantine approximation 
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O. N. German. Geometry of Diophantine exponents. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 2, pp. 273-347. http://geodesic.mathdoc.fr/item/RM_2023_78_2_a1/