Results 1 to 10 of about 343 (48)
On the continued fraction expansions of (1+pq)/2 and pq
Comptes rendus. Mathematique, 2021 The evenness and the values modulo 4 of the lengths of the periods of the continued fraction expansions of p p and √ 2p for p ≡ 3 (mod 4) a prime are known.
S. Louboutin
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Convergence properties of the classical and generalized Rogers-Ramanujan continued fraction [PDF]
Research in Number Theory, 2015 The aim of this paper is to study the convergence and divergence of the Rogers-Ramanujan and the generalized Rogers-Ramanujan continued fractions on the unit circle.
Emil-Alexandru Ciolan, R. A. Neiss
semanticscholar +2 more sources
Continued fractions related to a group of linear fractional transformations
Open Mathematics, 2023 There are strong relations between the theory of continued fractions and groups of linear fractional transformations. We consider the group G3,3{G}_{3,3} generated by the linear fractional transformations a=1−1∕za=1-1/z and b=z+2b=z+2.
Demir Bilal
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$q$-DEFORMED RATIONALS AND $q$-CONTINUED FRACTIONS
Forum of Mathematics, Sigma, 2020 We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$-deformed Pascal
SOPHIE MORIER-GENOUD, VALENTIN OVSIENKO
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Ramanujan and the Regular Continued Fraction Expansion of Real Numbers [PDF]
, 2004 In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^{3}}_{m}, ...
Laughlin, James Mc, Wyshinski, Nancy J.
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On the Rank of Universal Quadratic Forms over Real Quadratic Fields
Documenta Mathematica, 2018 We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field Q( √ D) and obtain lower and upper bounds for it in terms of certain sums of coefficients of the associated ...
V. Blomer, Vítězslav Kala
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Diophantine approximations and almost periodic functions
Demonstratio Mathematica, 2017 In this paper we investigate the asymptotic behaviour of the classical continuous and unbounded almost periodic function in the Lebesgue measure.Using diophantine approximations we show that this function can be estimated by functions of polynomial type ...
Nawrocki Adam
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Continued fractions and class number two
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 9, Page 565-571, 2001., 2001 We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm‐induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well‐known result by Hendy (1974) for complex quadratic
Richard A. Mollin
wiley +1 more source
Growth rate for the expected value of a generalized random Fibonacci sequence [PDF]
, 2008 A random Fibonacci sequence is defined by the relation g_n = | g_{n-1} +/- g_{n-2} |, where the +/- sign is chosen by tossing a balanced coin for each n. We generalize these sequences to the case when the coin is unbalanced (denoting by p the probability
Benoît Rittaud +7 more
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Two divisors of (n^2+1)/2 summing up to {\delta}n+{\epsilon}, for {\delta} and {\epsilon} even [PDF]
, 2014 In this paper we are dealing with the problem of the existence of two divisors of $(n^2+1)/2$ whose sum is equal to $\delta n+\varepsilon$, in the case when $\delta$ and $\varepsilon$ are even, or more precisely in the case in which $\delta\equiv ...
Bujačić, Sanda
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