Geodesic
Convergence sets of multidimensional local fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 125-133

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We study subsets of multidimensional local fields that have the property that any power series with coefficients from this subset converges when substituting an element of the maximum ideal for a variable. 
@article{ZNSL_2020_492_a8,
     author = {A. I. Madunts},
     title = {Convergence sets of multidimensional local fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--133},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a8/}
}
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A. I. Madunts. Convergence sets of multidimensional local fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 125-133. http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a8/