Normal integral basis of an unramified quadratic extension over a cyclotomic Z(2)-extension

作者：Ichimura Humio; Sumida Takahashi Hiroki

来源：Journal de Theorie des Nombres de Bordeaux, 2016, 28(2): 325-345.

Let l be an odd prime number. Let K/Q be a real cyclic extension of degree l, AK the 2-part of the ideal class group of K, and H/K the class field corresponding to A(K)/A(K)(2). Let K-n be the nth layer of the cyclotomic Z(2)-extension over K. We consider the questions (Q1) "does H/K has a normal integral basis?", and (Q2) "if not, does the pushed-up extension HKn/K-n has a normal integral basis for some n >= 1?" Under some assumptions on l and K, we answer these questions in terms of the 2-adic L-function associated to the base field K. We also give some numerical examples.

• 出版日期2016