On uniform approximation to successive powers of a real number
نویسندگان
چکیده
منابع مشابه
SIMULTANEOUS RATIONAL APPROXIMATION TO THE SUCCESSIVE POWERS OF A REAL NUMBER by Michel LAURENT
Let n be an integer ≥1 and let θ be a real number which is not an algebraic number of degree ≤ n/2 . We show that there exist >0 and arbitrary large real numbers X such that the system of linear inequalities |x0|≤X and |x0θ−xj |≤ X−1/ n/2 for 1≤j≤n, has only the zero solution in rational integers x0,...,xn. This result refines a similar statement due to H. Davenport and W. M. Schmidt, where the...
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— For a positive integer n and a real number ξ, let λn(ξ) denote the supremum of the real numbers λ such that there are arbitrarily large positive integers q such that ||qξ||, ||qξ2||, . . . , ||qξn|| are all less than q−λ. Here, || · || denotes the distance to the nearest integer. We study the set of values taken by the function λn and, more generally, we are concerned with the joint spectrum ...
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چکیده: در میان انواع متفاوتی از مبدل های آنالوگ به دیجیتال که تا کنون معرفی شده اند، مبدل های آنالوگ به دیجیتال تقاریب متوالی(sar ) به علت سادگی ساختار و همچنین توان مصرفی کم، همواره یکی از پرکاربرد ترین مبدل های آنالوگ به دیحیتال در کاربرد های بایومدیکال بوده اند. به همین دلیل تاکنون روش های متعددی برای کاهش هرچه بیشتر توان مصرفی در این مبدل ها ارائه شده است که در اکثر آنها توجهی به مشخصات سی...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2017
ISSN: 0019-3577
DOI: 10.1016/j.indag.2016.11.001