A remark on K-2 of the rings of integers of totally real number fields

作者：Guo Xuejun^*

来源：Communications in Algebra, 2007, 35(9): 2889-2893.

DOI：10.1080/00927870701404333

• Birch-Tate conjecture
• totally real number fields
• zeta function

Let F be a totally real number field with degree n = [F: Q] >= 3. Mazur and Urbanowicz proved that if
K2OF similar or equal to (Z/2Z)([F:Q]) (*)
and F is not Q(zeta(7) +zeta(-1)(7)) or Q(zeta(9) + zeta(-1)(9)), then F must be one of the 14 cases listed in Mazur and Urbanowicz (1992). In this article, it is proved that 3 of these 14 cases don't satisfy (*), while all the other cases satisfy (*). Hence we find all totally real number fields which satisfy (*).

• 出版日期2007
• 单位南京大学