Geodesic
The Stokes phenomenon for an irregular Gelfand-Kapranov-Zelevinsky system associated with a rank one lattice
Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1037-1063 Cet article a éte moissonné depuis la source Math-Net.Ru

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An explicit description of a multidimensional Stokes phenomenon for a Gelfand-Kapranov-Zelevinsky system associated with a lattice of rank one is given. Bibliography: 25 titles.
Keywords: Stokes phenomenon, multidimensional Pfaffian systems, Gelfand-Kapranov-Zelevinsky system, generalized hypergeometric functions. 
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D. V. Artamonov. The Stokes phenomenon for an irregular Gelfand-Kapranov-Zelevinsky system associated with a rank one lattice. Sbornik. Mathematics, Tome 207 (2016) no. 8, pp. 1037-1063. http://geodesic.mathdoc.fr/item/SM_2016_207_8_a0/

[1] P. Deligne, “Lettre à B. Malgrange du 20/12/1983”, Singularités irrégulières, Correspondance et documents, Doc. Math. (Paris), 5, Soc. Math. France, Paris, 2007, 37–41 | MR | Zbl

[2] B. Malgrange, “La classification des connexions irrégulières à une variable”, Mathematics and physics (Paris, 1979/1982), Progr. Math., 37, Birkhäuser, Boston, MA, 1983, 381–399 | MR | Zbl

[3] B. Malgrange, Équations différentielles à coefficients polynomiaux, Progr. Math., 96, Birkhäuser, Boston, MA, 1991, vi+232 pp. | MR | Zbl

[4] D. G. Babbitt, V. S. Varadarajan, Local moduli for meromorphic differential equations, Astérisque, 169–170, Soc. Math. France, Paris, 1989, 217 pp. | MR | Zbl

[5] C. Sabbah, Équations différetielles à points singuliers irréguliers et phénomène de Stokes en dimension 2, Asterisque, 263, Soc. Math. France, Paris, 2000, viii+190 pp. | MR | Zbl

[6] T. Mochizuki, Wild harmonic bundles and wild pure twistor ${D}$-modules, Asterisque, 340, Soc. Math. France, Paris, 2011, x+607 pp. | MR | Zbl

[7] C. Sabbah, Introduction to Stokes structures, Lecture Notes in Math., 2060, Springer-Verlag, Heidelberg, 2013, xiv+249 pp. | DOI | MR | Zbl

[8] H. Żoła̧dek, The monodromy group, Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series), 67, Birkhäuser, Basel, 2006, xii+580 pp. | MR | Zbl

[9] E. L. Ince, Ordinary differential equations, Longmans, London, 1926, viii+558 pp. | MR | Zbl

[10] A. S. Fokas, A. R. Its, A. A. Kapaev, V. Yu. Novokshenov, Painlevé transcendents. The Riemman–Hilbert approach, Math. Surveys Monogr., 128, Amer. Math. Soc., Providence, RI, 2006, xii+553 pp. | DOI | MR | Zbl

[11] A. Duval, C. Mitschi, “Matrices de Stokes et groupe de Galois des équations hypergéométriques confluentes généralisées”, Pacific J. Math., 138:1 (1989), 25–56 | DOI | MR | Zbl

[12] I. M. Gel'fand, A. V. Zelevinskii, M. M. Kapranov, “Hypergeometric functions and toral manifolds”, Funct. Anal. Appl., 23:2 (1989), 94–106 | DOI | MR | Zbl

[13] M. C. Fernández-Fernández, F. J. Castro-Jiménez, “Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve”, Trans. Amer. Math. Soc., 363:2 (2011), 923–948 | DOI | MR | Zbl

[14] M. C. Fernández-Fernández, F. J. Castro-Jiménez, “Gevrey solutions of irregular hypergeometric systems in two variables”, J. Algebra, 339 (2011), 320–335 | DOI | MR | Zbl

[15] Y. Sibuya, Linear differential equations in the complex domain: problems of analytic continuation, Transl. Math. Monogr., 82, Amer. Math. Soc., Providence, RI, 1990, xiv+269 pp. | MR | Zbl

[16] W. Jurkat, D. Lutz, A. Peyerimhoff, “Birkhoff invariants and effective calcualtions for meromorphic linear differential equations. I”, J. Math. Anal. Appl., 53:2 (1976), 438–470 | DOI | MR | Zbl

[17] W. B. Jurkat, D. A. Lutz, A. Peyerimhoff, “Birkhoff invariants and effective calculations for meromorphic linear differential equations. II”, Houston J. Math, 2:2 (1976), 207–238 | MR | Zbl

[18] W. Balser, W. B. Jurkat, D. A. Lutz, “Birkhoff invariants and Stokes' multipliers for meromorphic linear differential equations”, J. Math. Anal. Appl., 71:1 (1979), 48–94 | DOI | MR | Zbl

[19] R. Hotta, K. Takeuchi, T. Tanisaki, $D$-modules, perverse sheaves, and representation theory, Progr. Math., 236, Birkhäuser, Boston, MA, 2008, xii+407 pp. | DOI | MR | Zbl

[20] Y. André, “Structure des connexiones méromorphes formelles de plusieurs variables et semi-continuité de irrégularité”, Invent. Math., 170:1 (2007), 147–198 | DOI | MR | Zbl

[21] A. Erdélyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher transcendental functions, Based, in part, on notes left by H. Bateman, v. I, McGraw-Hill, New York–Toronto–London, 1953, xxvi+302 pp. | MR | MR | Zbl | Zbl

[22] Y. L. Luke, The special functions and their aproximations, v. 1, 2, Math. Sci. Eng., 53, Academic Press, New York–London, 1969, xx+349 pp., xx+485 pp. | MR | Zbl

[23] J. L. Fields, “The asymptotic expansion of the Meijer $G$-function”, Math. Comp., 26 (1972), 757–765 | DOI | MR | Zbl

[24] I. M. Gel'fand, M. I. Graev, V. S. Retakh, “General hypergeometric systems of equations and series of hypergeometric type”, Russian Math. Surveys, 47:4 (1992), 1–88 | DOI | MR | Zbl

[25] A. Adolphson, “Hypergeometric functions and rings generated by monomials”, Duke Math. J., 73:2 (1994), 269–290 | DOI | MR | Zbl