On linear recurrence relations satisfied by Pisot sequences
نویسندگان
چکیده
منابع مشابه
On Nearly Linear Recurrence Sequences
A nearly linear recurrence sequence (nlrs) is a complex sequence (an) with the property that there exist complex numbers A0,. . ., Ad−1 such that the sequence ( an+d + Ad−1an+d−1 + · · · + A0an )∞ n=0 is bounded. We give an asymptotic Binet-type formula for such sequences. We compare (an) with a natural linear recurrence sequence (lrs) (ãn) associated with it and prove under certain assumptions...
متن کاملOn Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or po...
متن کاملOn the multiplicity of linear recurrence sequences
We prove a lemma regarding the linear independence of certain vectors and use it to improve on a bound due to Schmidt on the zero-multiplicity of linear recurrence sequences. 1 Linear recurrence sequences Let {un}n∈Z be a linear recurrence sequence of complex numbers satisfying the recurrence relation un = c1un−1 + · · ·+ ctun−t, (1) for c1, . . . , ct ∈ C with ct 6= 0. We say it is of order t ...
متن کاملPalindromes in Linear Recurrence Sequences
We prove that for any base b ≥ 2 and for any linear homogeneous recurrence sequence {an}n≥1 satisfying certain conditions, there exits a positive constant c > 0 such that #{n ≤ x : an is palindromic in base b} x1−c.
متن کاملZeros of linear recurrence sequences
Let f (x) = P0(x)α 0 + · · · + Pk(x)α k be an exponential polynomial over a field of zero characteristic. Assume that for each pair i, j with i 6= j , αi/αj is not a root of unity. Define 1 = ∑kj=0(deg Pj +1). We introduce a partition of {α0, . . . , αk} into subsets { αi0, . . . , αiki } (1 ≤ i ≤ m), which induces a decomposition of f into f = f1 +· · ·+fm, so that, for 1 ≤ i ≤ m, (αi0 : · · ·...
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: Acta Arithmetica
سال: 1986
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-47-1-13-27