Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IM2_1991_36_1_a7, author = {A. N. Varchenko}, title = {The {Euler} beta-function, the {Vandermonde} determinant, {Legendre's} equation, and critical values of linear functions on a configuration of {hyperplanes.~II}}, journal = {Izvestiya. Mathematics }, pages = {155--167}, publisher = {mathdoc}, volume = {36}, number = {1}, year = {1991}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a7/} }
TY - JOUR AU - A. N. Varchenko TI - The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes.~II JO - Izvestiya. Mathematics PY - 1991 SP - 155 EP - 167 VL - 36 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a7/ LA - en ID - IM2_1991_36_1_a7 ER -
%0 Journal Article %A A. N. Varchenko %T The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes.~II %J Izvestiya. Mathematics %D 1991 %P 155-167 %V 36 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a7/ %G en %F IM2_1991_36_1_a7
A. N. Varchenko. The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes.~II. Izvestiya. Mathematics , Tome 36 (1991) no. 1, pp. 155-167. http://geodesic.mathdoc.fr/item/IM2_1991_36_1_a7/
[1] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. II, Nauka, M., 1984 | MR
[2] Varchenko A. N., “Kombinatorika i topologiya raspolozheniya affinnykh giperploskostei v veschestvennom prostranstve”, Funkts. analiz i ego prilozh., 21:1 (1987), 11–22 | MR | Zbl
[3] Varchenko A. N., “Funktsionalnye uravneniya dlya otobrazheniya ob'emov”, Matem zametki, 44:4 (1989), 417–427 | MR
[4] Varchenko A. N., “Opredelitel matritsy periodov gipergeometricheskikh integralov”, Uspekhi matem. nauk, 43:3 (1988), 240–241
[5] Varchenko A. N., “O mnogomernom opredelitele Vandermonda”, Uspekhi matem. nauk, 43:4 (1988), 190
[6] Varchenko A. N., “Opredelitel matritsy mnogomernykh gipergeometricheskikh integralov”, Dokl. AN CSSP, 308:4 (1989), 801–805 | MR
[7] Varchenko A. N., Gelfand I. M., “O funktsiyakh Khevisaida konfiguratsii giperploskostei”, Funkts. analiz i ego prilozh., 21:4 (1987), 1–18 | MR
[8] Vasilev V. A., Gelfand I. M., Zelevinskii A. V., “Algebraicheskie i kombinatornye aspekty obschei teorii gipergeometricheskikh funktsii”, Funkts. analiz i ego prilozh., 21:1 (1987), 23–38 | MR | Zbl
[9] Gelfand I. M., “Obschaya teoriya gipergeometricheskikh funktsii”, Dokl. AN SSSR, 288:1 (1986), 14–18 | MR | Zbl
[10] Gelfand I. M., Gelfand S. I., “Obobschennye gipergeometricheskie uravneniya”, Dokl. AN SSSR, 288:2 (1986), 279–283 | MR | Zbl
[11] Gelfand I. M., Zelevinskii A. V., “Obschie gipergeometricheskie funktsii na kompleksnykh grassmanianakh”, Funkts. analiz i ego prilozh., 20:3 (1986), 17–34 | MR | Zbl
[12] Gelfand I. M., Retakh V. S., Serganova V. V., “Obobschennye funktsii Eiri, kletki Shuberta i zhordanovy gruppy”, Dokl. AN SSSR, 298:1 (1988), 17–21 | MR | Zbl
[13] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, Vyp. 1, Fizmatgiz, M., 1959
[14] Givental A. B., “Skruchennye formuly Pikara–Lefshetsa”, Funkts. analiz i ego prilozh., 22:1 (1988), 12–22 | MR | Zbl
[15] Barnabei M., Brini A., Rota Dzh.-K., “Teoriya funktsii Mëbiusa”, Uspekhi matem. nauk, 41:3 (1986), 113–157 | MR | Zbl
[16] Uitteker E. T., Vatson G. N., Kurs sovremennogo analiza, GTTI, M., 1934
[17] Beitmen G., Erdein A., Vysshie transtsendentnye funktsii, Nauka, M., 1965
[18] Aomoto K., “On vanishing of cohomology attached to certain many valued meromorphic functions”, J. Math. Soc. Japan, 27 (1975), 248–255 | DOI | MR | Zbl
[19] Aomoto K., “Les equations aux differences lineaires et Ies integrates des functions multiformes”, J. of the Fac. of Sci. Univ. of Tokyo, 22 (1975), 271–297 | MR | Zbl
[20] Aomoto K., “On the Structure of Integrals of Power Product of Linear Functions”, Sc. Papers of the College of General Education University of Tokyo, 27:2 (1977), 49–61 | MR | Zbl
[21] Aomoto K., “Addition Theorem of Abel Type for Hyper – logarithms”, Nagoya Math. J., 88 (1982), 55–71 | MR | Zbl
[22] Aomoto K., “Configurations and Invariant Theory of Gauss–Manin Systems”, Group Representations and Systems of Differential Equations, Advanced Study in Pure Math., 4, 1984, 165–179 | MR | Zbl
[23] Borel A. et al., “Algebraic $D$-moduls”, Perspective in Math., 2 (1987) | MR
[24] Deligne P., “Equation differentielles a points singuliers reguliers”, Lecture Notes in Math., 163 (1970) | MR | Zbl
[25] Esnault H., Viehweg E., Vanishing and non-vanishing theorems, Preprint/Max-Planck-Institut für Mathematik, 1987 | MR
[26] Barlet D., Varchenko A., Around the intersection form of an isolated singularity of hypersurface, Preprint/Universite de Nancy, 1986 | MR
[27] Varchenko A. N., “Beta-funktsiya Eilera, opredelitel Vandermonda, uravnenie Lezhandra i kriticheskie znacheniya lineinykh funktsii na konfiguratsii giperploskostei. I”, Izv. AN SSSR. Ser. matem., 53:6 (1989), 1206–1235 | MR | Zbl