منابع مشابه
Periodic Continued Fractions And
We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form
متن کاملPeriodic Continued Fractions in Elliptic Function Fields
We construct all families of quartic polynomials over Qwhose square root has a periodic continued fraction expansion, and detail those expansions. In particular we prove that, contrary to expectation, the cases of period length nine and eleven do not occur. We conclude by providing a list of examples of pseudo-elliptic integrals involving square roots of polynomials of degree four. The primary ...
متن کاملPurely Periodic Nearest Square Continued Fractions
We give three sets of conditions to determine whether a real quadratic surd ξ = (P + √ D)/Q has a purely periodic nearest square continued fraction expansion. One set is a few inequalities involving only ξ and its conjugate ξ = (P − √ D)/Q. Another set is a few inequalities involving only P/ √ D and Q/ √ D. A third set of conditions and additional results are presented.
متن کاملProblems on periodic simple continued fractions.
Let N be a positive non-square integer and a(1),a(2),...,a(3) be the partial denominators in the period of length s = s(N) of the continued fraction for radicalN. Also let Sigma(N) = a(3) - a(3-1) + -... +/- a(1), and let h(d) be the class-number of Q( radicald). Hirzebruch (unpublished) recently found the surprising theorem (which is a special case of more general results): If p is a prime ide...
متن کاملPeriodic Continued Fractions and Kronecker Symbols
We study the Kronecker symbol ( s t ) for the sequence of the convergents s/t of a purely periodic continued fraction expansion. Whereas the corresponding sequence of Jacobi symbols is always periodic, it turns out that the sequence of Kronecker symbols may be aperiodic. Our main result describes the period length in the periodic case in terms of the period length of the sequence of Jacobi symb...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1986
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000022716