Geodesic
On functions of several complex variables that are separately meromorphic
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 481-489 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper it is proved that a function of $n$ complex variables that is meromorphic in each variable separately on a special set $X$ is globally meromorphic in the neighborhood of $X$. This result is an analog of a theorem of J. Siciak on separate holomorphicity. Bibliography: 8 titles. 
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     author = {M. V. Kazaryan},
     title = {On functions of several complex variables that are separately meromorphic},
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M. V. Kazaryan. On functions of several complex variables that are separately meromorphic. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 481-489. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a2/

[1] J. Siciak, “Separately analitic functions and envelopes of holomorphy of some lower dimensional subsets of $\mathbf{C}^n$”, Ann. Pol. Math., 22:2 (1969), 145–170 | MR

[2] W. Rothstein, “Ein neuer Beweis des Hartogsschen Hauptsatzes und seine Ausdehnung auf meromorphe Functionen”, Math. Z., 53 (1950), 84–95 | DOI | MR | Zbl

[3] E. Sakai, “A note on meromorphic functions in several complex variables”, Mem. Fac. Sci., Kyusyu Univ., ser. A, 11:1 (1957), 75–80 | MR | Zbl

[4] S. Bokhner, U. T. Martin, Funktsii mnogikh kompleksnykh peremennykh, IL, Moskva, 1951

[5] H. Okuda, E. Sakai, “On the continuation theorem of Levi and the radius of meromorphy”, Mem. Fac. Sci., Kyusyu Univ., ser. A, 11:1 (1957), 65–73 | MR | Zbl

[6] I. Kajiwara, “On weak Poincaré problem”, Mem. Fac. Sci., Kyusyu Univ., ser. A, 22 (1968), 9–17 | MR | Zbl

[7] M. Brelo, Osnovy klassicheskoi teorii potentsiala, izd-vo «Mir», Moskva, 1964 | MR

[8] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, izd-vo «Nauka», Moskva, 1966 | MR