منابع مشابه
Periodic 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...
متن کاملA Note on Jacobi Symbols and Continued Fractions
1. INTRODUCTION. It is well known that the continued fraction expansion of a real quadratic irrational is periodic. Here we relate the expansion for √ rs, under the assumption that rX
متن کاملOn the Distribution of Continued Fractions and Modular Symbols
Using the techniques introduced by D. Mayer, we prove an extension of the classical Gauss–Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take into account some congruence properties of consecutive convergents. We then study some averages related to modular symbols. §0. Introduction and summary 0.1. Continued fractions. We start by fixing the nota...
متن کاملEvaluation of Certain Legendre Symbols
We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p 6= 2, and ab = p − 1, then the Legendre symbol ( b p ) is given by ( b p ) = (−1).
متن کاملPeriodic 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1991
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-59-4-365-379