Computation of the Infimum in the Littlewood Conjecture
نویسنده
چکیده
The famous Littlewood Conjecture states that for any two real numbers (α, β) ∈ R the value m(α, β) := inf { q · ||qα|| · ||qβ|| : q ∈ N} is equal to zero. In this paper we provide an algorithm which for given 2 > 0 checks, if the value mLC := supα,β m(α, β) is less than 2. In particular with its help we show that mLC < 1/19. We also provide a similar algorithm for p-adic counterpart of the Littlewood Conjecture and show that an analogue of mLC in 2-adic case is at most 1/9.
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عنوان ژورنال:
- Experimental Mathematics
دوره 25 شماره
صفحات -
تاریخ انتشار 2016