New irrationality measures for q-logarithms
نویسندگان
چکیده
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
منابع مشابه
An essay on irrationality measures of π and other logarithms
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...
متن کاملAn Essay on Irrationality Measures of Logarithms
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 ...
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-...
متن کاملIRRATIONALITY MEASURES FOR CERTAIN q-MATHEMATICAL CONSTANTS
We prove sharp irrationality measures for a q-analogue ofπ and related q-series, and indicate open problems on linear and algebraic independence of the series that might be viewed as q-analogues of some classical mathematical constants.
متن کاملEULER’S CONSTANT, q-LOGARITHMS, AND FORMULAS OF RAMANUJAN AND GOSPER
The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values of the q-logarithm function, with natural choice of q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Comput.
دوره 75 شماره
صفحات -
تاریخ انتشار 2006