Irrationality measure of sequences
نویسندگان
چکیده
منابع مشابه
An Irrationality Measure for Regular Paperfolding Numbers
Let F(z) = ∑ n>1 fnz n be the generating series of the regular paperfolding sequence. For a real number α the irrationality exponent μ(α), of α, is defined as the supremum of the set of real numbers μ such that the inequality |α − p/q| < q−μ has infinitely many solutions (p, q) ∈ Z × N. In this paper, using a method introduced by Bugeaud, we prove that μ(F(1/b)) 6 275331112987 137522851840 = 2....
متن کاملIRRATIONALITY MEASURE AND LOWER BOUNDS FOR π(x)
One of the most important functions in number theory is π(x), the number of primes at most x. Many of the proofs of the infinitude of primes fall naturally into one of two categories. First, there are those proofs which provide a lower bound for π(x). A classic example of this is Chebyshev’s proof that there is a constant c such that cx/ log x ≤ π(x). Another method of proof is to deduce a cont...
متن کاملRational Irrationality
We present a game-theoretic account of irrational agent behavior and define conditions under which irrational behavior may be considered quasi-rational. To do so, we use a 2-player, zero-sum strategic game, parameterize the reward structure and study how the value of the game changes with this parameter. We argue that for any “underdog” agent, there is a point at which the asymmetry of the game...
متن کاملDiamonds, Compactness, and Measure Sequences
We establish the consistency of the failure of the diamond principle on a cardinal κ which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of κ in a Radin generic extension.
متن کاملAperiodicity Measure for Infinite Sequences
We introduce the notion of aperiodicity measure for in nite symbolic sequences. Informally speaking, the aperiodicity measure of a sequence is the maximum number (between 0 and 1) such that this sequence di ers from each of its non-identical shifts in at least fraction of symbols being this number. We give lower and upper bounds on the aperiodicity measure of a sequence over a xed alphabet. We ...
متن کاملذخیره 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: Hiroshima Mathematical Journal
سال: 2005
ISSN: 0018-2079
DOI: 10.32917/hmj/1150998271