A deformation of commutative polynomial algebras in even numbers of variables
Open Mathematics (2010)
- Volume: 8, Issue: 1, page 73-97
- ISSN: 2391-5455
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] Andrews G.F., Askey R., Roy R., Special functions. Encyclopedia of Mathematics and its Applications, 71, Cambridge University Press, Cambridge, 1999
- [2] Bass H., Connell E., Wright D., The Jacobian conjecture, reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc., 1982, 7, 287–330 http://dx.doi.org/10.1090/S0273-0979-1982-15032-7 Zbl0539.13012
- [3] Björk J.-E., Rings of differential operators, North-Holland Publishing Co., Amsterdam-New York, 1979
- [4] Coutinho S.C., A primer of algebraic D-modules, London Mathematical Society Student Texts, 33, Cambridge University Press, Cambridge, 1995 Zbl0848.16019
- [5] Dunkl C., Xu Y., Orthogonal polynomials of several variables, Encyclopedia of Mathematics and its Applications, 81, Cambridge University Press, Cambridge, 2001
- [6] van den Essen A., Polynomial automorphisms and the Jacobian conjecture, Progress in Mathematics, 190, Birkhäuser Verlag, Basel, 2000 Zbl0962.14037
- [7] Filaseta M., Lam T.-Y., On the irreducibility of the generalized Laguerre polynomials, Acta Arith., 2002, 105(2), 177–182 http://dx.doi.org/10.4064/aa105-2-4 Zbl1010.12001
- [8] Keller O.H., Ganze Gremona-Transformationen, Monats. Math. Physik, 1939, 47(1), 299–306 (in German) http://dx.doi.org/10.1007/BF01695502
- [9] Laguerre E., Sur l′ intégrale , Bull. Soc. Math. France, 1879, 7, reprinted in Oeuvres, 1971, 1, 428–437 (in French)
- [10] Pólya G., Szegö G., Problems and theorems in analysis, Vol. II,, Revised and enlarged translation by C.E. Billigheimer of the fourth German edition, Springer Study Edition, Springer-Verlag, New York-Heidelberg, 1976 Zbl0359.00003
- [11] Schur I., Einige Sätze über Primzahlen mit Anwendungen auf Irreduzibilitätsfragen, I, Sitzungsber. Preuss. Akad. Wiss. Berlin Phys.-Math. Kl., 1929, 14, 125–136 (in German) Zbl55.0069.03
- [12] Schur I., Affektlose Gleichungen in der Theorie der Laguerreschen und Hermiteschen Polynome, Journal für die reine und angewandte Mathematik, 1931, 165, 52–58 (in German) http://dx.doi.org/10.1515/crll.1931.165.52 Zbl57.0125.05
- [13] Szegö G., Orthogonal Polynomials, 4th edition, American Mathematical Society, Colloquium Publications, Vol. XXIII, American Mathematical Society, Providence, R.I., 1975
- [14] Wolfram Research, http://functions.wolfram.com/Polynomials/LaguerreL/
- [15] Wolfram Research, http://functions.wolfram.com/Polynomials/LaguerreL3/
- [16] Zhao W., Hessian Nilpotent Polynomials and the Jacobian Conjecture, Trans. Amer. Math. Soc., 2007, 359(1), 249–274 http://dx.doi.org/10.1090/S0002-9947-06-03898-0 Zbl1109.14041
- [17] Zhao W., A Vanishing Conjecture on Differential Operators with Constant Coefficients, Acta Mathematica Vietnamica, 2007, 32(3), 259–285 Zbl1139.14303
- [18] Zhao W., Images of commuting differential operators of order one with constant leading coefficients, preprint available at http://arxiv.org/abs/0902.0210 Zbl1197.14064
- [19] Zhao W., Generalizations of the Image Conjecture and the Mathieu Conjecture, J. Pure Appl. Algebra, doi:10.1016/j.jpaa.2009.10.007 Zbl1205.33017
- [20] Zhao W., New Proofs for the Abhyankar-Gujar Inversion Formula and the Equivalence of the Jacobian Conjecture and the Vanishing Conjecture, preprint available at http://arxiv.org/abs/0907.3991