A note on Lacunary polynomials
نویسندگان
چکیده
منابع مشابه
A Note on Lacunary Lonely Runners
We give a simple argument proving the lonely runner conjecture in the case where the speed of the runners forms a certain lacunary sequence. This improves an earlier result by Pandey, and is then used to derive that for each number of runners the lonely runner conjecture is true for a set of nonzero measure in a natural probability space.
متن کاملA note on lacunary series in $mathcal{Q}_K$ spaces
In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.
متن کاملOn testing the divisibility of lacunary polynomials by cyclotomic polynomials
An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficientexponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.
متن کاملFactoring bivariate sparse (lacunary) polynomials
We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K[x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial in the bit length of the sparse encoding of the input and in d . Moreover, we show that the factors over Q of degree ≤ d which are not binomials can also be computed in tim...
متن کاملDivisibility Test for Lacunary Polynomials
Given two lacunary (i.e. sparsely-represented) polynomials with integer coefficients, we consider the decision problem of determining whether one polynomial divides the other. In the manner of Plaisted [6], we call this problem 2SparsePolyDivis. More than twenty years ago, Plaisted identified as an open problem the question of whether 2SparsePolyDivis is in P [7]. Some progress has been made si...
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: Bulletin of the American Mathematical Society
سال: 1948
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1948-09038-3