Results 1 to 10 of about 5,581 (50)
Algebraic Independence and Mahler's method [PDF]
, 2011 We give some new results on algebraic independence within Mahler's method, including algebraic independence of values at transcendental points. We also give some new measures of algebraic independence for infinite series of numbers.
Becker +7 more
core +4 more sources
Hankel determinants, Pad\'e approximations, and irrationality exponents
, 2015 The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$.
Bugeaud, Yann +3 more
core +1 more source
, 2017 We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first two
Kammeyer, Holger
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Exponents of Diophantine Approximation and Sturmian Continued Fractions [PDF]
, 2004 Let x be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents w_n(x) and w_n^*(x) defined by Mahler and Koksma.
Bugeaud, Yann, Laurent, Michel
core +5 more sources
Thue's Fundamentaltheorem, I: The General Case
, 2010 In this paper, Thue's Fundamentaltheorem is analysed. We show that it includes, and often strengthens, known effective irrationality measures obtained via the so-called hypergeometric method as well as showing that it can be applied to previously ...
Voutier, Paul
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Report on some recent advances in Diophantine approximation [PDF]
, 2009 A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
core +3 more sources
On Mahler's transcendence measure for $e$
, 2018 We present a completely explicit transcendence measure for $e$. This is a continuation and an improvement to the works of Borel, Mahler and Hata on the topic.
Ernvall-Hytönen, Anne-Maria +2 more
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, 1998 Creativity is said to be highly desired in post-modern and post-industrial organizations Creativity and anarchy on the one hand, and managerialism, on the other, can be seen as different forms of knowledge, two opposed ideals.
Alexandersson Ola +33 more
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Average Characteristic Polynomials of Determinantal Point Processes [PDF]
, 2015 We investigate the average characteristic polynomial $\mathbb E\big[\prod_{i=1}^N(z-x_i)\big] $ where the $x_i$'s are real random variables which form a determinantal point process associated to a bounded projection operator.
Hardy, Adrien
core +2 more sources
Diophantine approximation of Mahler numbers
, 2015 Suppose that $F(x)\in\mathbb{Z}[[x]]$ is a Mahler function and that $1/b$ is in the radius of convergence of $F(x)$. In this paper, we consider the approximation of $F(1/b)$ by algebraic numbers.
Bell, Jason +2 more
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