On certain infinite families of imaginary quadratic fields whose Iwasawa λ-invariant is equal to 1

Abstract

Let p be an odd prime number. In this paper, we show existence of certain infinite families of imaginary quadratic fields in which p splits and whose Iwasawa λinvariant of the cyclotomic Z p -extension is equal to 1.

Reports on families of imaginary abelian fields with pseudo-null unramified Iwasawa modules

“…When p ≥ 5, By Horie-Ôhnishi's result [10], there is an imaginary quadratic field F such that the prime p splits in F/Q and that p ∤ h F . Alternatively, Ito [11] showed that the class numbers of imaginary quadratic fields Q( √ 1 − p) and Q( √ 4 − p) are not divisible by p, see lemma 2.4 of [11], hence we can choose…”