On the 2-primary part of K₂ of rings of integers in certain quadratic number fields

• Autorzy: A. Vazzana
• Języki publikacji: EN

Abstrakty

EN

1. Introduction. For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of $K₂𝓞_E$. For quadratic fields whose discriminant has arbitrarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form $ℚ(√(p₁ ...p_k))$, where the primes $p_i$ are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrelbrink which examines under what conditions the 4-rank of $K₂𝓞_E$ is zero for such fields. In the course of proving the theorem, we will see how the conditions can be easily computed.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 80
• Numer: 3
• Strony: 225-235

Daty

wydano

1997

otrzymano

1996-06-08

Twórcy

autor

A. Vazzana

• Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.

Bibliografia

• [BC] P. Barrucand and H. Cohn, Note on primes of type x² + 32y², class number and residuacity, J. Reine Angew. Math. 238 (1969), 67-70.
• [CH1] P. E. Conner and J. Hurrelbrink, Class Number Parity, Ser. Pure Math. 8, World Sci., Singapore, 1988.
• [CH2] P. E. Conner and J. Hurrelbrink, Examples of quadratic number fields with K₂𝓞 containing no element of order four, circulated notes, 1989.
• [CH3] P. E. Conner and J. Hurrelbrink, The 4-rank of K₂𝓞, Canad. J. Math. 41 (1989), 932-960.
• [CH4] P. E. Conner and J. Hurrelbrink, On elementary abelian 2-Sylow K₂ of rings of integers of certain quadratic number fields, Acta Arith. 73 (1995), 59-65.
• [H] J. Hurrelbrink, Circulant graphs and 4-ranks of ideal class groups, Canad. J. Math. 46 (1994), 169-183.