Abstract
The main purpose of this article is to introduce the notion of real quadratic fields of minimal type in terms of continued fractions with period l . We show that fundamental units of real quadratic fields that are not of minimal type are relatively small. So, we see by a theorem of Siegel that such fields have relatively large class numbers. Also, we show that there exist exactly 51 real quadratic fields of class number 1 that are not of minimal type, with one more possible exception. All such fields are listed in the table of Section 8.2. Therefore we study real quadratic fields with period l of minimal type in order to find real quadratic fields of class number 1 , and first examine the case where l≤4 . In particular we obtain a result on Yokoi invariants m d and class numbers h d of real quadratic fields Q( d ) with period 4 of minimal type.
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