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A Note On Structure of Certain Real Quadratic Number Fields | ||
| Iranian Journal of Science | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1394 | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2015.3381 | ||
| نویسنده | ||
| Özen ÖZER* | ||
| Kırklareli University Faculty of Art and Sciences Department of Mathematics | ||
| چکیده | ||
| The aim of this paper is to determine the general forms of the continued fraction expansions of the quadratic irrational number which is integral basis element of Z[√d] , also determine which are the coefficents of fundamental units of the real quadratic number field Q(√d) by using a new explicit formulation. Fundamental units can be calculated with this algorithm in an easy way in the period which is equal to 9 in the continued fraction expansion of for such quadratic fields where d≡1(mod4) is a positive square free integer. Moreover, some results will be given for both Yokoi’s invariant value of which is defined in terms of coefficents of fundamental unit and the class number of the real quadratic number fields Q(√d) as well as reduced indefinite quadratic forms f_d. | ||
| کلیدواژهها | ||
| Fraction؛ Fundamental Unit؛ Class Number؛ Quadratic Forms | ||
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آمار تعداد مشاهده مقاله: 888 |
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