Geodesic
Diophantine approximations of linear forms
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 5-24

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Diophantine approximations of linear combinations with real algebraic numbers of arbitrary degree are considered. Using the recurrence relation it is possible to generate an infinite sequence of integer approximations of the linear forms. We prove that the resulting Diophantine approximations are the best relative to some polyhedral norms that are ray functions or the Minkowski functionals. 
@article{ZNSL_2020_490_a0,
     author = {V. G. Zhuravlev},
     title = {Diophantine approximations of linear forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--24},
     publisher = {mathdoc},
     volume = {490},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a0/}
}
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V. G. Zhuravlev. Diophantine approximations of linear forms. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 5-24. http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a0/