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For a non-square positive integer d with 4 ∤ d, put ω(d) :=(1 + √<d>)/2 if d is congruent to 1 modulo 4 and ω(d) := √<d> otherwise. Let a_1, a_2, . . . , a_<ℓ-1> be the symmetric part of the simple co...ntinued fraction expansion of ω(d). We say that the sequence a_1, a_2, . . . , a_<[ℓ/2]> is the primary symmetric part of the simple continued fraction expansion of ω(d). A notion of ‘ELE type' for a finite sequence was introduced in Kawamoto et al (Comment. Math. Univ. St. Pauli 64(2) (2015), 131-155). The aims of this paper are to introduce a notion of ‘pre-ELE type' for a finite sequence and to give a way of constructing primary symmetric parts of ELE type. As a byproduct, we show that there exist infinitely many real quadratic fields with period ℓ of minimal type for each even ℓ ≥ 6.続きを見る
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