On divisibility of the class number h + of the real cyclotomic fields ( ζ p + ζ p - 1 ) by primes q < 10000

Pavel Trojovský

Mathematica Slovaca (2000)

  • Volume: 50, Issue: 5, page 541-555
  • ISSN: 0232-0525

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Trojovský, Pavel. "On divisibility of the class number $h^+$ of the real cyclotomic fields $\mathbb {Q}(\zeta _p+\zeta _p^{-1})$ by primes $q < 10000$." Mathematica Slovaca 50.5 (2000): 541-555. <http://eudml.org/doc/32309>.

@article{Trojovský2000,
author = {Trojovský, Pavel},
journal = {Mathematica Slovaca},
keywords = {class number; cyclotomic field; computation; divisibility},
language = {eng},
number = {5},
pages = {541-555},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On divisibility of the class number $h^+$ of the real cyclotomic fields $\mathbb \{Q\}(\zeta _p+\zeta _p^\{-1\})$ by primes $q < 10000$},
url = {http://eudml.org/doc/32309},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Trojovský, Pavel
TI - On divisibility of the class number $h^+$ of the real cyclotomic fields $\mathbb {Q}(\zeta _p+\zeta _p^{-1})$ by primes $q < 10000$
JO - Mathematica Slovaca
PY - 2000
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 50
IS - 5
SP - 541
EP - 555
LA - eng
KW - class number; cyclotomic field; computation; divisibility
UR - http://eudml.org/doc/32309
ER -

References

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  2. ESTES D. R., On the parity of the class number of the field of q-th roots of unity, Rocky Mountain J. Math. 19 (1989), 675-681. (1989) Zbl0703.11052MR1043240
  3. JAKUBEC S., On divisibility of class number or real abelian fields of prime conductor, Abh. Math. Sem. Univ. Hamburg 63 (1993), 67-86. (1993) MR1227865
  4. JAKUBEC S., On Divisibility of h+ by the prime 3, Rocky Mountain J. Math. 24 (1994), 1467-1473. (1994) MR1322239
  5. JAKUBEC S., On Divisibility of h+ by the prime 5, Math. Slovaca 44 (1994), 650-700. (1994) MR1338435
  6. JAKUBEC S., Connection between Wiefferich congruence and divisibility of h+, Acta Arith. 71 (1995), 55-64. (1995) MR1338671
  7. JAKUBEC S., Connection between congruences nq-1 = 1 (mod q2) and divisibility of h+, Abh. Math. Sem. Univ. Hamburg 66 (1996), 151-158. (1996) MR1418226
  8. JAKUBEC S., On divisibility of the class number h+ of the real cyclotomic fields of prime degree I, Math. Comp. 67 (1998), 396-398. (1998) MR1443121
  9. JAKUBEC S.-TROJOVSKY P., On divisibility of the class number h+ of the real cyclotomic fields Q(C + Cp1) by primes q <= 5000, Abh. Math. Sem. Univ. Hamburg 67 (1997), 269-280. (1997) MR1481542
  10. METSÄNKYLÄ T., An application of the p-adic class number formula, Manuscripta Math. 93 (1997), 481-498. (1997) Zbl0886.11061MR1465893
  11. VAN DER LINDEN F., Class number computations of real abelian number fields, Math. Comp. 39 (1982), 693-707. (1982) Zbl0505.12010MR0669662
  12. WAGSTAFF S. S., The irregular primes to 125000, Math. Comp. 32 (1978), 583-592. (1978) Zbl0377.10002MR0491465
  13. WASHINGTON L. C., Introduction to Cyclotomic Fields, Grad Texts in Math., Springer-Verlag, New York-Heidelberg-Berlin, 1982. (1982) Zbl0484.12001MR0718674

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