Michael Schlosser's Home Page

Dr. Michael J. Schlosser _X
Fakultät für Mathematik
Universität Wien
Nordbergstraße 15
A-1090 Vienna
Austria _XXXX
telephone: (+43-1) 4277-506/47
fax: (+43-1) 4277-9-506
e-mail:

Vorlesungen im laufenden Semester (vergangenen Semester).    Courses in the current semester (last semester).

Informationsseite zur Vorlesung und den Übungen Lineare Algebra und Geometrie für LAK.
Informationsseite zur Vorlesung und den Übungen Einführung in die lineare Algebra und Geometrie.
Informationsseite zur Vorlesung und den Übungen Mathematik 2 für LA Informatik.

Scientific publications (in reverse chronological order):

• Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture (jointly with Robin Langer and S. Ole Warnaar) [SIGMA 5 (2009), 055, 20 pp.]
• Recurrence formulas for Macdonald polynomials of type A (jointly with Michel Lassalle) [J. Algebraic Combin., to appear]
• Multilateral inversion of A_r, C_r and D_r basic hypergeometric series [Ann. Comb. 13 (2009), 341-363]
• On an identity by Chaundy and Bullard. I (jointly with Tom H. Koornwinder) [Indag. Math. (N.S.) 19 (2) (2008), 239-261]
• A Taylor expansion theorem for an elliptic extension of the Askey-Wilson operator [in Special Functions and Orthogonal Polynomials (D. Dominici and R. S. Maier, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 471 (2008), 175-186]
• A new multivariable ₆ψ₆ summation formula [Ramanujan J. 17 (3) (2008), 305-319]
• Curious extensions of Ramanujan's ₁ψ₁ summation formula (jointly with Victor J. W. Guo) [J. Math. Anal. Appl. 334 (1) (2007), 393-403]
• Macdonald polynomials and multivariable basic hypergeometric series [Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, SIGMA 3 (2007), 056, 30 pp.]
• Elliptic enumeration of nonintersecting lattice paths [J. Combin. Theory Ser. A 114 (3) (2007), 505-521]
• Some curious q-series expansions and beta integral evaluations (jointly with George Gasper) [Ramanujan J. 13 (1-3) (2007), 229-242]
• Elliptic determinant evaluations and the Macdonald identities for affine root systems (jointly with Hjalmar Rosengren) [Compos. Math. 142 (4) (2006), 937-961]
• Noncommutative hypergeometric and basic hypergeometric equations (jointly with Alessandro Conflitti) [14 pp., submitted]
• Noncommutative extensions of Ramanujan's ₁ψ₁ summation [Electron. Trans. Numer. Anal. 24 (2006), 94-102]
• Summation formulae for noncommutative hypergeometric series [35 pp., submitted]
• Explicit computation of the q,t-Littlewood-Richardson coefficients [Proceedings of the Workshop on Jack, Hall-Littlewood and Macdonald polynomials (V. Kuznetsov and S. Sahi, eds.) Edinburgh, ICMS, Sept. 23-26, 2003; Contemp. Math. 417 (2006), 335-343]
• Inversion of the Pieri formula for Macdonald polynomials (jointly with Michel Lassalle) [Adv. Math. 202 (2) (2006), 289-325]
• Summation, transformation, and expansion formulas for multibasic theta hypergeometric series (jointly with George Gasper) [Adv. Stud. Contemp. Math. (Kyungshang) 11 (2005), no. 1, 67-84; also in Proceedings of the Workshop Elliptic Integrable Systems (M. Noumi and K. Takasaki, eds.) Kyoto, RIMS, 2004; Rokko Lectures in Mathematics 18 (2005), 1-17]
• Another proof of Bailey's ₆ψ₆ summation (jointly with Frédéric Jouhet) [Aequationes Math. 70 (1-2) (2005), 43-50]
• On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series (jointly with Hjalmar Rosengren) [J. Comput. Appl. Math. 178 (2005), 377-391]
• Abel-Rothe type generalizations of Jacobi's triple product identity [in Theory and Applications of Special Functions. A Volume Dedicated to Mizan Rahman (M. E. H. Ismail and E. Koelink, eds.), Dev. Math. 13 (2005), 383-400]
• q-Analogues of the sums of consecutive integers, squares, cubes, quarts and quints [Electron. J. Combin. 11 (1) (2004), #R71, 12 pp.]
• Some curious extensions of the classical beta integral evaluation [in Mathematics and Computer Science, III (M. Drmota, P. Flajolet, D. Gardy, B. Gittenberger, eds.) Vienna, 2004; Trends Math., Birkhäuser, Basel, 2004, pp. 59-68]
• An analytic formula for Macdonald polynomials (jointly with Michel Lassalle) [C. R. Math. Acad. Sci. Paris 337 (9) (2003), 569-574]
• Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations (jointly with Hjalmar Rosengren) [Indag. Math. (N.S.) 14 (2003), 483-514]
• A nonterminating ₈φ₇ summation for the root system C_r [J. Comput. Appl. Math. 160 (2003), 283-296]
• Inversion of bilateral basic hypergeometric series [Electron. J. Combin. 10 (2003), #R10, 27 pp.]
• A multidimensional generalization of Shukla's ₈ψ₈ summation [Constr. Approx. 19 (2003), 163-178]
• Elementary derivations of identities for bilateral basic hypergeometric series [Selecta Math. (N.S.) 9 (2003) 1, 119-159]
• A new A_n extension of Ramanujan's ₁ψ₁ summation with applications to multilateral basic hypergeometric series (jointly with Stephen C. Milne) [in Special Functions 2000 (J. Bustoz and S. K. Suslov, eds.), Rocky Mount. J. Math. 32 (2) (2002), 759-792]
• A simple proof of Bailey's very-well-poised ₆ψ₆ summation [Proc. Amer. Math. Soc. 130 (2002), 1113-1123]
• Multilateral transformations of q-series with quotients of parameters that are nonnegative integral powers of q [in q-Series with Applications to Combinatorics, Number Theory, and Physics (B. C. Berndt and K. Ono, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 291 (2001), 203-227]
• A new multidimensional matrix inversion in A_r [in q-Series from a Contemporary Perspective (M. E. H. Ismail and D. Stanton, eds.), Amer. Math. Soc., Providence, R. I., Contemp. Math. 254 (2000), 413-432]
• Summation theorems for multidimensional basic hypergeometric series by determinant evaluations [Discrete Math. 210 (2000), 151-169]
• Some new applications of matrix inversions in A_r [Ramanujan J. 3 (1999), 405-461]
• A new multidimensional matrix inverse with applications to multiple q-series (jointly with Christian Krattenthaler) [(H. W. Gould Anniversary Volume) Discrete Math. 204 (1999), 249-279; selected to be included in Discrete Math., spec. vol. ``Editors' Choice, Edition 1999'']
• Multidimensional matrix inversions and multiple basic hypergeometric series associated to root systems [in Special functions and differential equations (K. Srinivasa Rao, R. Jagannathan, G. Vanden Berghe, and J. Van der Jeugt, eds.), Proceedings of a workshop, WSSF '97, Madras, India, January 13-24, 1997; Allied Publ., New Delhi (1998), 25-30]
• C_n and D_n very-well-poised ₁₀φ₉ transformations (jointly with Gaurav Bhatnagar) [Constr. Approx. 14 (1998), 531-567]
• Multidimensional matrix inversions and A_r and D_r basic hypergeometric series [Ramanujan J. 1 (1997), 243-274]
• Multidimensional matrix inversions [Sém. Lothar. Combin. 35 (1995), B35g, 24 pp.]

Theses:

• Derivation of single and multivariable q-series identities, habilitation thesis, University of Vienna, 2004.
• Multidimensional matrix inversions and multiple basic hypergeometric series, Ph.D. thesis, University of Vienna, 1996.
• Symmetrieklassen von Plane Partitions, master thesis (in German), University of Vienna, 1993.