Geodesic
Series of hypergeometric type and discriminants
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 540-548.

Voir la notice de l'article provenant de la source Math-Net.Ru

The monomial of solutions of a reduced system of algebraic equations are series of hypergeometric type. The Horn–Karpranov result for hypergeometric series is extended to the case of series of hypergeometric type.
Keywords: series of hypergeometric type, reduced system
Mots-clés : logarithmic Gauss map, discriminant locus, conjugative radii of convergence. 
@article{JSFU_2023_16_4_a11,
     author = {Quang Khanh Phan},
     title = {Series of hypergeometric type and discriminants},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {540--548},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a11/}
}
TY  - JOUR
AU  - Quang Khanh Phan
TI  - Series of hypergeometric type and discriminants
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2023
SP  - 540
EP  - 548
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a11/
LA  - en
ID  - JSFU_2023_16_4_a11
ER  - 
%0 Journal Article
%A Quang Khanh Phan
%T Series of hypergeometric type and discriminants
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2023
%P 540-548
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a11/
%G en
%F JSFU_2023_16_4_a11
Quang Khanh Phan. Series of hypergeometric type and discriminants. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 4, pp. 540-548. http://geodesic.mathdoc.fr/item/JSFU_2023_16_4_a11/

[1] I.A.Antipova, A.K.Tsikh, “The discriminant locus of a system of n Laurent polynomials in n variables”, Izv. Math., 76:5 (2012), 881–906 | DOI | MR | Zbl

[2] K.Aomoto et al., Theory of Hypergeometric Functions, Springer Monographs in Mathematics, Springer, Japan, 2011 | DOI | MR | Zbl

[3] P.Appell, “On hypergeometric functions of two variables”, Resal J., 8:3 (1882), 173–216

[4] W.N.Bailey, Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics, 32, 1964 | MR

[5] H.Bateman, A.Erdelyi, Higher transcendental functions, v. 1, McGraw-Hill, New York, 1953

[6] A.N.Cherepanskiy, A.K.Tsikh, “Convergence of two-dimensional hypergeometric series for algebraic functions”, Integral Transforms and Special Functions, 31:10 (2020), 838–855 | DOI | MR | Zbl

[7] I.M Gelfand, M.I.Graev, V.S.Retakh, “General hypergeometric systems of equations and series of hypergeometric type”, Uspekhi Mat. Nauk, 47:4 (1992), 3–82 (in Russian) | MR | Zbl

[8] J.Horn, “Über die Convergenz der hypergeometrischen Reihen zweier und dreier Veräderlichen”, Mathematische Annalen, 34 (1889), 544–600 | DOI | MR

[9] M.M.Kapranov, “A characterization of A-discriminantal hypersurfaces in terms of the logarithmic Gauss map”, Math. Ann., 290 (1991), 277–285 | DOI | MR | Zbl

[10] V.R.Kulikov, V.A.Stepanenko, “On solutions and Waring's formulas for systems of n algebraic equations for n unknowns”, St. Petersburg Mathematical Journal, 26:5 (2015), 839–848 | DOI | MR | Zbl

[11] G.Lauricella, “Sulle funzioni ipergeometriche a piu variabili”, Rend. Circ. Mat. Palermo, 7, 1893, 111–158 (Italian) | DOI

[12] M.Passare, A.K.Tsikh, Amoebas: their spines and their contours, Contemporary Mathematics, 377, eds. G. L. Litvinov, V. P. Maslov, AMS, 2005 | MR | Zbl

[13] T.M.Sadykov, A.K.Tsikh, Hypergeometric and algebraic functions of several variables, Nauka, M., 2014 (in Russian)

[14] G.A.Sarkissian, V.P.Spiridonov, “Rational hypergeometric identities”, Funct. Anal. Appl., 55:3 (2021), 250–255 | DOI | MR | Zbl

[15] M.Sato, T.Shintani, “Theory of prehomogeneous vector spaces (algebraic part) – the English translation of Sato's lecture from Shintani's note”, Nagoya Mathematical Journal, 120 (1990), 1–34 | DOI | MR | Zbl

[16] B.V.Shabat, Introduction to Complex Analysis, Translations of mathematical monographs, American Math. Society, 1992 | DOI | MR | Zbl