Gcd-closed sets and determinants of matrices associated with arithmetical functions
نویسندگان
چکیده
منابع مشابه
Arithmetical properties of polynomials associated with the lemniscate elliptic functions.
1 Bellman, R., "Wigert's Approximate Functional Equation and the Riemann ZetaFunction," Duke Math. J., 16, 547-552 (1949). 2 Hardy, G. H., "On Dirichlet's Divisor Problem," Proc. Lond. Math. Soc., 15, 1-20 (1916). 3Hardy, G. H., "Some Multiple Integrals," Quart. J. Math., 39, 357-375 (1908). 4Maass, H., "Uber eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichet...
متن کاملMass Problems Associated with Effectively Closed Sets
The study of mass problems and Muchnik degrees was originally motivated by Kolmogorov’s non-rigorous 1932 interpretation of intuitionism as a calculus of problems. The purpose of this paper is to summarize recent investigations into the lattice of Muchnik degrees of nonempty effectively closed sets in Euclidean space. Let Ew be this lattice. We show that Ew provides an elegant and useful framew...
متن کاملK -Trivial Closed Sets and Continuous Functions
We investigate the notion of K-triviality for closed sets and continuous functions. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial Π 1 class with no computable elements. For any K-trivial degree d, there is a K-trivial continuous function of degree d.
متن کاملDivisibilty Properties of Gcd Ve Lcm Matrices
Let a, b and n be positive integers and let S = {x1, x2, . . . , xn} be a set of distinct positive integers. The n × n matrix (Sf ) = (f ((xi, xj))), having f evaluated at the greatest common divisor (xi, xj) of xi and xj as its ij−entry, is called the GCD matrix associated with f on the set S. Similarly, the n × n matrix [Sf ] = (f ([xi, xj ])) is called the LCM matrix associated with f on S. ...
متن کاملDeterminants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
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: 2002
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa101-4-2