Geodesic
On determinant representations of Hermite--Pad\'e polynomials
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 83 (2022) no. 1, pp. 17-35

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In this work we introduce new concepts: weakly normal index, weakly perfect system of functions. With these concepts for an arbitrary system of power series we formulate and prove criteria for the uniqueness of solutions to two Hermite–Padé problems, and obtain explicit determinant representations of Hermite–Padé types 1 and 2 polynomials. Proven statements complement well-known results in Hermite–Padé approximation theory. 
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     author = {A. P. Starovoitov and N. V. Ryabchenko},
     title = {On determinant representations of {Hermite--Pad\'e} polynomials},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/MMO_2022_83_1_a1/}
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A. P. Starovoitov; N. V. Ryabchenko. On determinant representations of Hermite--Pad\'e polynomials. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 83 (2022) no. 1, pp. 17-35. http://geodesic.mathdoc.fr/item/MMO_2022_83_1_a1/