Results 1 to 10 of about 78 (60)
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
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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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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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Number Theory And Formal Languages [PDF]
, 1999 . I survey some of the connections between formal languages and number theory. Topics discussed include applications of representation in base k, representation by sums of Fibonacci numbers, automatic sequences, transcendence in finite characteristic ...
Jeffrey Shallit
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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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Linear Fractional Transformations of Continued Fractions with Bounded Partial Quotients [PDF]
, 1996 Let ` be a real number with continued fraction expansion ` = [a 0 ; a 1 ; a 2 ; : : :], and let M = " a b c d # be a matrix with integer entries and with j det(M)j 6= 0. If ` has bounded partial quotients, then a`+b c`+d = [a 0 ; a 1 ; a
J. O. Shallit +3 more
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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
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Pattern Classification of Continued Fractions With Square Number as Base
Journal of Physics: Conference Series, 2019 In number theory, study of number sequences is an enthusiastic area. Among these the sequence of polygonal numbers gives a unique richness in is applicability. Polygonal numbers which have both order, rank of are of various dimensions. Here, the study is
A. Venkatachalam, P. Balamurugan
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