On the mean values of certain trigonometrical polynomials II
نویسندگان
چکیده
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 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 کاملOn Polynomials Characterized by a Certain Mean Value Property
for xER, 0<t<ex (R denotes an «-dimensionaI region; x and yt are abbreviations for (xi, • • • , x„), (yn, • • • , ytn))We assume that the y<'s span £„ so that I^m^JV. We furthermore assume, without loss of generality, that yi, • • • , y« are linearly independent. Friedman and Littman [5] have recently shown that V consists of polynomials of degrees ^N(N—l)/2. This bound is actually attained whe...
متن کاملValues of coefficients of cyclotomic polynomials II
Let a(n, k) be the kth coefficient of the nth cyclotomic polynomial. In part I it was proved that {a(mn, k) | n ≥ 1, k ≥ 0} = Z, in case m is a prime power. In this paper we show that the result also holds true in case m is an arbitrary positive integer.
متن کاملOn Locally Repeated Values of Certain Arithmetic Functions . Ii
which is nearly 1 if K is large . Thus if n and n+1 both satisfy (1 .3) and if we view v(n) and v(n+l) as "independent events", then the "probability" that (L2) holds should be at least (2K Vlog log n)-1 . Summing these probabilities would then give order of magnitude x1f log log x solutions n of (1 .2) with n-x, thus supporting the conjecture. A refinement of this heuristic argument even sugge...
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: Illinois Journal of Mathematics
سال: 1962
ISSN: 0019-2082
DOI: 10.1215/ijm/1255631803