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1. arXiv:1212.1733 (Published 2012-12-07)

   Notes on the divisibility of the class numbers of certain imaginary quadratic fields

   Akiko Ito
   Comments: 27 pages

   Categories: math.NT

   Subjects: 11R11, 11R29

   Keywords: imaginary quadratic fields, class number, divisibility, infinite families
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   In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

2. arXiv:1212.1392 (Published 2012-12-06)

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

   Akiko Ito
   Comments: 51 pages

   Categories: math.NT

   Subjects: 11R11, 11R23, 11R29

   Keywords: imaginary quadratic fields, infinite families, odd prime number, cyclotomic zp-extension
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   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 {\lambda}-invariant of the cyclotomic Zp-extension is equal to 1.