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Displaying 961 – 980 of 1538

On the Ramanujan AGM fraction. II: The complex-parameter case.

Borwein, J., Crandall, R. (2004)

Experimental Mathematics

On the random character of fundamental constant expansions.

Bailey, David H., Crandall, Richard E. (2001)

Experimental Mathematics

On the rational approximation to the Thue–Morse–Mahler numbers

Yann Bugeaud (2011)

Annales de l’institut Fourier

Let ${(t_{k})}_{k \geq 0}$ be the Thue–Morse sequence on ${0, 1}$ defined by $t_{0} = 0$ , $t_{2 k} = t_{k}$ and $t_{2 k + 1} = 1 - t_{k}$ for $k \geq 0$ . Let $b \geq 2$ be an integer. We establish that the irrationality exponent of the Thue–Morse–Mahler number $\sum_{k \geq 0} t_{k} b^{- k}$ is equal to $2$ .

On the sets of uniqueness of a distribution function of {ξ(p/q)ⁿ}

S. D. Adhikari, P. Rath, N. Saradha (2005)

Acta Arithmetica

On the simultaneous approximation of $a$ , $b$ and $a^{b}$

A. Bijlsma (1977)

Compositio Mathematica

On the simultaneous approximation of certain numbers.

K. Väänänen (1977)

Journal für die reine und angewandte Mathematik

On the simultaneous diophantine approximation of values of certain algebraic functions

Charles Osgood (1971)

Acta Arithmetica

On the simultaneous diophantine approximation of values of certain hypergeometric and algebraic functions

Charles Osgood (1974)

Acta Arithmetica

On the spacing between terms of generalized Fibonacci sequences

Diego Marques (2014)

Colloquium Mathematicae

For k ≥ 2, the k-generalized Fibonacci sequence $(F ₙ^{(k)}) ₙ$ is defined to have the initial k terms 0,0,...,0,1 and be such that each term afterwards is the sum of the k preceding terms. We will prove that the number of solutions of the Diophantine equation $F ₘ^{(k)} - F ₙ^{(ℓ)} = c > 0$ (under some weak assumptions) is bounded by an effectively computable constant depending only on c.

On the sum of consecutive cubes being a perfect square

R. J. Stroeker (1995)

Compositio Mathematica

On the sums of continued fractions

Bohuslav Diviš (1973)

Acta Arithmetica

On the system of Diophantine equations $a^{2} + b^{2} = {(m^{2} + 1)}^{r}$ and $a^{x} + b^{y} = {(m^{2} + 1)}^{z}$

Florian Luca (2012)

Acta Arithmetica

On the System of Diophantine Equations X2 - 6y2 = -5 and x= 2z2 - 1.

Maurice Mignotte, Attila Pethö (1995)

Mathematica Scandinavica

On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces

Eduard Wirsing (1974)

Acta Arithmetica

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

For a real number $q > 1$ and a positive integer $m$ , let $Y_{m} (q) : = \{\sum_{i = 0}^{n} ϵ_{i} q^{i} : ϵ_{i} \in \{0, \pm 1, ..., \pm m\}, n = 0, 1, ...\}$ . In this paper, we show that $Y_{m} (q)$ is dense in $ℝ$ if and only if $q < m + 1$ and $q$ is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].