Linear independence of 'logarithms' in linear varieties
نویسندگان
چکیده
منابع مشابه
On the linear independence measure of logarithms of rational numbers
In this paper we give a general theorem on the linear independence measure of logarithms of rational numbers and, in particular, the linear independence measure of 1, log 2, log 3, log 5 and of 1, log 2, log 3, log 5, log 7. We also give a method to search for polynomials of smallest norm on a real interval [a, b] which may be suitable for computing or improving the linear independence measure ...
متن کاملLinear Independence of q-Logarithms over the Eisenstein Integers
For fixed complex q with |q| > 1, the q-logarithm Lq is the meromorphic continuation of the series ∑ n>0 z / q −1 , |z| < |q|, into the whole complex plane. IfK is an algebraic number field, one may ask if 1, Lq 1 , Lq c are linearly independent over K for q, c ∈ K× satisfying |q| > 1, c / q, q2, q3, . . .. In 2004, Tachiya showed that this is true in the Subcase K Q, q ∈ Z, c −1, and the prese...
متن کاملLinear Independence Measures for Logarithms of Algebraic Numbers
Hence we are back to the problem of estimating from below the distance between 1 and a number of the form α1 1 · · ·αbn n . The first three lectures are devoted to the qualitative theory of transcendental numbers, the last three ones to the quantitative theory of Diophantine approximation. According to Hermite-Lindemann’s Theorem, a number Λ = β − logα, with algebraic α and β, is zero only in t...
متن کاملon the effect of linear & non-linear texts on students comprehension and recalling
چکیده ندارد.
15 صفحه اولnon-linear study of various slit shear walls in steel structures
seismic retrofit strategies have been developed in the past few decades following the introduction of new seismic provisions and the availability of advanced materials and methods. it can be observed that new approaches to deal with more lateral forces are more innovative and more energy absorbent. in line with this, there is a growing trend toward the use of steel shear walls as a system with ...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1980
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-36-4-407-417