80
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On the Jacobians of Curves Defined by the Generalized Laguerre Polynomials

References

  • [Berger et al. 17] L. Berger et al. “Explicit Arithmetic of Jacobians of Generalized Legendre Curves over Global Function Fields.” Preprint, arXiv:1505.00021, American Mathematical Society, 2017.
  • [Bray et al. 13] J. Bray, D. Holt, C. Roney-Dougal. The Maximal Subgroups of the Low-Dimensional Finite Classical Groups. With a Foreword by Martin Liebeck, vol. 407, London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, 2013.
  • [Coleman 87] R. F. Coleman. “On the Galois Groups of the Exponential Taylor Polynomials.” Enseign. Math. 33: 3–4 (1987), 183–189.
  • [Conway et al. 85] J. Conway et al. ATLAS of Finite Groups. Cambridge: Oxford University Press, 1985.
  • [Dieulefait 02] L. Dieulefait. “Explicit Determination of the Images of the Galois Representations Attached to Abelian Surfaces with End(A)=Z.” Exp. Math. 11: 4 (2002), 503–512.
  • [Dokchitser and Dokchitser 12] T. Dokchitser, V. Dokchitser. “Surjectivity of mod 2n Representations of Elliptic Curves.” Math. Z. 272: 3–4 (2012), 961–964.
  • [Elkies 06] N. Elkies. “Elliptic Curves with 3-Adic Galois Representation Surjective Mod 3 but not Mod 9.” Preprint, arXiv:math/0612734, December 2006.
  • [Filaseta and Lam 02] M. Filaseta and T.-Y. Lam. “On the Irreducibility of the Generalized Laguerre Polynomials.” Acta Arith. 105: 2 (2002), 177–182.
  • [Garrett 97] P. Garrett. Buildings and Classical Groups. London: Chapman & Hall, 1997.
  • [Gow 89] R. Gow. “Some Generalized Laguerre Polynomials whose Galois Groups are the Alternating Groups.” J. Number Theory 31: 2 (1989), 201–207.
  • [Hajir 09] F. Hajir. “Algebraic Properties of a Family of Generalized Laguerre Polynomials.” Canad. J. Math. 61: 3 (2009), 583–603.
  • [Hajir and Wong 06] F. Hajir, S. Wong. “Specializations of One-Parameter Families of Polynomials.” Ann. Inst. Fourier (Grenoble) 56: 4 (2006), 1127–1163.
  • [Hindry and Silverman 00] M. Hindry, J. Silverman. Diophantine Geometry. An Introduction. Graduate Texts in Mathematics, vol. 201. New York: Springer-Verlag, 2000.
  • [Katz 15] N. Katz. “Wieferich Past and Future.” In Topics in Finite Fields, vol. 632, pp. 253–270, Contemporary Mathematics. Providence, RI: Amer. Math. Soc., 2015.
  • [Landesman 17a] A. Landesman, A. Swaminathan, J. Tao, Y. Xu. “Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of their Jacobians.” Preprint, arXiv:1705.08777, May 2017a.
  • [Landesman 17b] A. Landesman, A. Swaminathan, J. Tao, Y. Xu. “Lifting Subgroups of Symplectic Groups over Z/ℓZ.” Preprint, arXiv:1607.04698v2, Research in Number Theory, 2017b.
  • [L-Functions XX] L-Functions and Modular Forms Database. lmfdb.org.
  • [Liu 94] Q. Liu. “Conducteur et discriminant minimal de courbes de genre 2.” Compos. Math., 94 (1994), 51–79. https://www.math.u-bordeaux.fr/qliu/G2R/index.html.
  • [Magma Online XX] Magma Online Calculator. http://magma.maths.usyd.edu.au/calc/.
  • [Milne and Waterhouse 71] J.S. Milne, W.C. Waterhouse. “Abelian Varieties over Finite Fields.” In 1969 Number Theory Institute, vol. XX, pp. 53–64, Proceedings of Symposia in Pure Mathematics Series, State University, New York, Stony Brook, NY, 1969). Providence, RI: Amer. Math. Soc., 1971.
  • [Mitchell 14] H. Mitchell. “The Subgroups of the Quaternary Abelian Linear Group.” Trans. Amer. Math. Soc. 15: 4 (1914), 379–396.
  • [Ohkouchi and Sakai 04] M. Ohkouchi, F. Sakai. “The Gonality of Singular Plane Curves.” Tokyo J. Math. 27: 1 (2004), 137–147.
  • [Pyle 95] E. Pyle. “Abelian Varieties over the Set of Rational Numbers with Large Endomorphism Algebras and Their Simple Components over the Set of Irrational Numbers.” PhD Diss., University of California, Berkeley, 1995.
  • [Sakai 93] F. Sakai. “Singularities of Plane Curves.” Geometry of Complex Projective Varieties (Cetraro, 1990), vol. 9, pp. 257–273, Sem. Conf. Rende: Mediterranean, 1993.
  • [Schur 73a] I. Schur. Gleichungen Ohne Affekt, Gesammelte Abhandlungen. Band III, pp. 191–197. Berlin: Springer, 1973a.
  • [Schur 73b] I. Schur. Affektlose Gleichungen in der Theorie der Laguerreschen und Hermiteschen Polynome, Gesammelte Abhandlungen. Band III, pp. 227–233, Berlin: Springer, 1973b.
  • [Sell 04] E. Sell. “On a Certain Family of Generalized Laguerre Polynomials.” J. Number Theory 107: 2 (2004), 266–281.
  • [Serre 00] J-P. Serre. Oeuvres, vol. 4, pp. 1–55. Berlin: Springer-Verlag, 2000.
  • [Serre 98] J-P. Serre. “Abelian ℓ-adic Representations and Elliptic Curves.” Research Notes in Mathematics, edited by A. K. Peters, Ltd., Wellesley, MA, 1998.
  • [Wong 05] S. Wong. “On the Genus of Generalized Laguerre Polynomials.” J. Algebra 288: 2 (2005), 392–399.
  • [Yelton 15] J. Yelton. “Hyperelliptic Jacobians and Their Associated ℓAdic Galois Representations.” PhD diss. Pennsylvania State University, 2015.
  • [Zywina 15] D. Zywina. “An Explicit Jacobian of Dimension 3 with Maximal Galois Action.” Preprint arXiv:1508.07655v1, August 2015.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.