New irrationality measures for $q$-logarithms
نویسندگان
چکیده
منابع مشابه
New irrationality measures for q-logarithms
The three main methods used in diophantine analysis of q-series are combined to obtain new upper bounds for irrationality measures of the values of the q-logarithm function
متن کاملConvergents and Irrationality Measures of Logarithms
We prove new irrationality measures with restricted denominators of the form dbνmcB m (where B,m ∈ N, ν > 0, s ∈ {0, 1} and dm = lcm{1, 2, . . . , m}) for values of the logarithm at certain rational numbers r > 0. In particular, we show that such an irrationality measure of log(r) is arbitrarily close to 1 provided r is sufficiently close to 1. This implies certain results on the number of non-...
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produces ‘good’ rational approximations to log a. There are several ways of perfoming integration in (1) in order to show that the integrals lies in Q log a + Q; we give an exposition of different methods below. The aim of this essay is to demonstrate how suitable generalizations of the integrals in (1) allow to prove the best known results on irrationality measures of the numbers log 2, π and ...
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produces ‘good’ rational approximations to log a. There are several ways of performing integration in (1) in order to show that the integral lies in Q log a+ Q; we give an exposition of different methods below. The aim of this essay is to demonstrate how suitable generalizations of the integrals in (1) allow to prove the best known results on irrationality measures of the numbers log 2, π and l...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2005
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-05-01812-0