Quintic Polynomials and Real Cyclotomic Fields with Large Class Numbers

  title={Quintic Polynomials and Real Cyclotomic Fields with Large Class Numbers},
  author={Ren{\'e} Schoof and Lawrence C. Washington},
We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime p = 641491 the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an appendix we give a characterization of the "simplest" quadratic, cubic and quartic fields. 

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Connection between Gaussian periods and cyclic units," Math

  • Comp., v. 50,
  • 1988
Highly Influential
15 Excerpts


  • C. WASHINGTON, "Class numbers of cyclotomic…
  • 1985
2 Excerpts

Solved and Unsolved Problems in Number Theory, 3rd ed., Chelsea

  • New York,
  • 1985


  • E. Seah, L. C. Washingto
  • C. Williams, "The calculation of a large cubic…
  • 1983
2 Excerpts

CUSICK, "Lower bounds for regulators," in Number Theory, Noordwijkerhout

  • T W.
  • Proceedings of the Journées Arithmétiques…
  • 1983
1 Excerpt

Class numbers of real cyclotomic fields," Math

  • Comp., v. 39,
  • 1982
2 Excerpts

WASHINGTON, Introduction to Cyclotomic Fields, Graduate Texts

  • L C.
  • in Math.,
  • 1982

Nombre de classes d'une extension cyclique réelle de Q, de degré 4 ou 6 et de conducteur premier," Math

  • C. MOSER
  • Nachr., v. 102,
  • 1981
1 Excerpt

PAYAN, "Majoration du nombre de classes d'un corps cubique cyclique de conducteur premier,

  • C. MOSER, J.-J
  • J. Math. Soc Japan, v
  • 1981
1 Excerpt

GRAS, "Calcul du nombre de classes et des unités des extensions abéliennes réelles de Q,

  • G. GRAS, ¿ M.-N
  • Bull. Sei. Math., v
  • 1977
1 Excerpt

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