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 ∫
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We consider the set σP of the power non-negative polynomials of several variables.By QP we denote the class of the polynomials from σ1 which can be represented as a sum of squares.It is shown in the classic work by D.Hilbert[3] that QP does not coincide with σP .Step by step a number of polynomials belonging to σP but not belonging to QP was constructed(see[4]-[6]).It is interesting to note tha...
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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 ...
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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...
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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.
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1937
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-28-1-131-166