On localization in Kronecker’s diophantine theorem
نویسنده
چکیده
Using a probabilistic approach, we extend for general Q-linearly independent sequences a result of Túran concerning the sequence (log p ℓ), p ℓ being the ℓ-th prime. For instance let λ 1 , λ 2 ,. .. be linearly independent over Q. We prove that there exists a constant C 0 such that for any positive integers N and ω, if T > 4ω
منابع مشابه
An Effective Version of Kronecker’s Theorem on Simultaneous Diophantine Approximation
Kronecker’s theorem states that if 1, θ1, . . . , θn are real algebraic numbers, linearly independent over Q, and if α ∈ R, then for any > 0 there are q ∈ Z and p ∈ Z such that |qθi − αi − pi| < . Here, a bound on q is given in terms of the dimension n, of the precision , of the degree of the θi’s and of their height. A possible connection to the square-root sum problem is discussed.
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