Let n be a positive integer. In this paper we estimate the size of the set of linear forms b 1 log a 1 + b 2 log a 2 + โข โข โข + b n log a n , where |b i | B i and 1 a i A i are integers, as A i , B i โ โ.
On Algebraic Numbers of Small Height: Linear Forms in One Logarithm
โ Scribed by M. Mignotte; M. Waldschmidt
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 522 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let S be the union of all CM-fields and S 0 be the set of non-zero algebraic numbers of S which are not roots of unity. We show that in S 0 Weil's height cannot be bounded from below by an absolute constant.
Gao, G.-G., On consecutive numbers of the same height in the Collatz problem, Discrete Mathematics 112 (1993) 261-267. The Collatz function C(n) is defined to take odd numbers n to 3n + 1 and even numbers n to n/2. This note presents computational results on consecutive numbers that have the same h
fields, the problem is essentially a planar lattice point problem (cf. ZAGIER [17]). To this, the deep results of HUXLEY [3], [4] can be applied to get For cubic fields, W. MULLER [12] proved that ## 43 - (h the class number), using a deep exponential sum technique due to KOLESNIK [7]. every n