منابع مشابه
On Mean Values of Dirichlet Polynomials
We show the following general lower bound valid for any positive integer q, and arbitrary reals φ1, . . . , φN and non-negative reals a1, . . . , aN , cq ( N ∑ n=1 a 2 n )q ≤ 1 2T ∫
متن کاملOn Existence of Boundary Values of Polyharmonic Functions
In trigonometric series terms all polyharmonic functions inside the unit disk are described. For such functions it is proved the existence of their boundary values on the unit circle in the space of hyperfunctions. The necessary and sufficient conditions are presented for the boundary value to belong to certain subspaces of the space of hyperfunctions. The purpose of this paper is to find neces...
متن کاملSquarefree Values of Polynomials
where m is any integer > n:We will be interested in estimating the number of polynomials f(x) for which there exists an integer m such that f(m) is squarefree. This property should hold for all polynomials f(x) for which Nf is squarefree. However, this seems to be very di cult to establish. Nagel [8] showed that if f(x) 2 Z[x] is an irreducible quadratic and Nf is squarefree, then f(m) is squar...
متن کاملPolynomials Assuming Square Values
If f(x1, ..., xn) ∈ Z[x1, ..., xn] has the property that every integer specialization gives an integral square value, then f is itself the square of a polynomial. We also give an effective version of this result by using an effective version of a classical theorem of E. Noether along with a theorem of Lang and Weil.
متن کاملSome Results on the Field of Values of Matrix Polynomials
In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...
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: Michigan Mathematical Journal
سال: 1957
ISSN: 0026-2285
DOI: 10.1307/mmj/1028990180