Algebraic properties of a family of Jacobi polynomials
John Cullinan[1]; Farshid Hajir[2]; Elizabeth Sell[3]
- [1] Department of Mathematics Bard College Annandale-On-Hudson, NY 12504
- [2] Department of Mathematics University of Massachusetts Amherst MA 01003
- [3] Department of Mathematics Millersville University P.O. Box 1002 Millersville, PA 17551
Journal de Théorie des Nombres de Bordeaux (2009)
- Volume: 21, Issue: 1, page 97-108
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topReferences
top- S. Ahlgren, K. Ono, Arithmetic of singular moduli and class polynomials. Compos. Math. 141 (2005), 283–312. Zbl1133.11036MR2134268
- J. Brillhart, P. Morton, Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial. J. Number Theory. 106 (2004), 79–111. Zbl1083.11036MR2049594
- R. Coleman, On the Galois groups of the exponential Taylor polynomials. L’Enseignement Math. 33 (1987), 183–189. Zbl0672.12004MR925984
- J.D. Dixon, B. Mortimer, Permutation Groups. Springer-Verlag, 1996. Zbl0951.20001MR1409812
- F. Hajir, Algebraic properties of a family of generalized Laguerre polynomials. To appear in Canad. J. Math. Zbl1255.33006MR2514486
- F. Hajir, On the Galois group of generalized Laguerre polynomials. J. Théor. Nombres Bordeaux 17 (2005), 517–525. Zbl1094.11042MR2211305
- F. Hajir, S. Wong, Specializations of one-parameter families of polynomials. Annales de L’Institut Fourier. 56 (2006), 1127-1163. Zbl1160.12004MR2266886
- M. Hindry, J. Silverman, Diophantine Geometry, An Introduction. Springer-Verlag, 2000. Zbl0948.11023MR1745599
- M. Kaneko, D. Zagier, Supersingular -invariants, hypergeometric series, and Atkin’s orthogonal polynomials. In Computational perspectives on number theory. AMS/IP Stud. Adv. Math. 7 (1998), 97–126. Zbl0955.11018MR1486833
- M. Liebeck, C. Praeger, J. Saxl, A classification of the maximal subgroups of the finite alternating and symmetric groups. J. Algebra 111 (1987), no. 2, 365–383. Zbl0632.20011MR916173
- K. Mahlburg, K. Ono, Arithmetic of certain hypergeometric modular forms. Acta Arith. 113 (2004), 39–55. Zbl1100.11015MR2046967
- P. Müller, Finiteness results for Hilbert’s irreducibility theorem. Ann. Inst. Fourier 52 (2002), 983–1015. Zbl1014.12002MR1926669
- I. Schur, Affektlose Gleichungen in der Theorie der Laguerreschen und Hermitschen Polynome. Gesammelte Abhandlungen. Band III, 227–233, Springer, 1973. Zbl0002.11501
- I. Schur. Gessammelte Abhandlungen Vol. 3, Springer, 1973 Zbl0274.01054
- E. Sell, On a family of generalized Laguerre polynomials. J. Number Theory 107 (2004), 266–281. Zbl1053.11083MR2072388
- G. Szegö, Orthogonal Polynomials, 4th ed. Providence, RI: Amer. Math. Soc., 1975. Zbl0305.42011
- S. Wong, On the genus of generalized Laguerre polynomials. J. Algebra. 288 (2005), no. 2, 392–399. Zbl1078.33009MR2146136