On D 5 -polynomials with integer coefficients

Yasuhiro Kishi[1]

  • [1] Department of Mathematics Fukuoka University of Education 1-1 Bunkyoumachi Akama, Munakata-shi Fukuoka, 811-4192 Japan

Annales mathématiques Blaise Pascal (2009)

  • Volume: 16, Issue: 1, page 113-125
  • ISSN: 1259-1734

Abstract

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We give a family of D 5 -polynomials with integer coefficients whose splitting fields over ℚ are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.

How to cite

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Kishi, Yasuhiro. "On $D_5$-polynomials with integer coefficients." Annales mathématiques Blaise Pascal 16.1 (2009): 113-125. <http://eudml.org/doc/10564>.

@article{Kishi2009,
abstract = {We give a family of $D_5$-polynomials with integer coefficients whose splitting fields over $\mathbb\{Q\}$ are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.},
affiliation = {Department of Mathematics Fukuoka University of Education 1-1 Bunkyoumachi Akama, Munakata-shi Fukuoka, 811-4192 Japan},
author = {Kishi, Yasuhiro},
journal = {Annales mathématiques Blaise Pascal},
keywords = {class number; Fibonacci number; polynomial; imaginary quadratic field},
language = {eng},
month = {1},
number = {1},
pages = {113-125},
publisher = {Annales mathématiques Blaise Pascal},
title = {On $D_5$-polynomials with integer coefficients},
url = {http://eudml.org/doc/10564},
volume = {16},
year = {2009},
}

TY - JOUR
AU - Kishi, Yasuhiro
TI - On $D_5$-polynomials with integer coefficients
JO - Annales mathématiques Blaise Pascal
DA - 2009/1//
PB - Annales mathématiques Blaise Pascal
VL - 16
IS - 1
SP - 113
EP - 125
AB - We give a family of $D_5$-polynomials with integer coefficients whose splitting fields over $\mathbb{Q}$ are unramified cyclic quintic extensions of quadratic fields. Our polynomials are constructed by using Fibonacci, Lucas numbers and units of certain cyclic quartic fields.
LA - eng
KW - class number; Fibonacci number; polynomial; imaginary quadratic field
UR - http://eudml.org/doc/10564
ER -

References

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  7. S. Nakamura, A microcosm of Fibonacci numbers (Japanese), (2002), Nippon Hyoronsha Co., Tokyo 
  8. Charles J. Parry, On the class number of relative quadratic fields, Math. Comp. 32 (1978), 1261-1270 Zbl0401.12008MR502013
  9. Paulo Ribenboim, The new book of prime number records, (1996), Springer-Verlag, New York Zbl0856.11001MR1377060
  10. Masahiko Sase, On a family of quadratic fields whose class numbers are divisible by five, Proc. Japan Acad. Ser. A Math. Sci. 74 (1998), 120-123 Zbl0926.11081MR1658854
  11. P. J. Weinberger, Real quadratic fields with class numbers divisible by n , J. Number Theory 5 (1973), 237-241 Zbl0287.12007MR335471
  12. Yoshihiko Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), 57-76 Zbl0222.12003MR266898

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