On the Sidon constant for Dirichlet polynomials
نویسندگان
چکیده
منابع مشابه
The Sidon Constant for Homogeneous Polynomials
The Sidon constant for the index set of nonzero m-homogeneous polynomials P in n complex variables is the supremum of the ratio between the l norm of the coefficients of P and the H(D) norm of P . We present an estimate which gives the right order of magnitude for this constant, modulo a factor depending exponentially on m. We use this result to show that the Bohr radius for the polydisc D is b...
متن کاملOn the Supremum of Random Dirichlet Polynomials
logN . One can refer to Bohr [B], Bohnenblust and Hille [BH], Helson [H], Hardy and Riesz [HR], Queffélec [Q3] for this background and related results. This of course, basically justifies the investigation of the supremum of Dirichlet polynomials (see for instance Konyagin and Queffélec [KQ]). The following classical reduction step enables to replace the Dirichlet polynomial by some relevant tr...
متن کاملThe Sidon constant of sets with three elements
We solve an elementary minimax problem and obtain the exact value of the Sidon constant for sets with three elements {n0, n1, n2}: it is sec(π/2n) for n = max |ni − nj |/ gcd(n1 − n0, n2 − n0).
متن کاملOn 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 the Supremum of Random Dirichlet Polynomials with Multiplicative Coefficients
We study the average supremum of some random Dirichlet polynomials DN (t) = ∑ N n=1 εnd(n)n , where (εn) is a sequence of independent Rademacher random variables, the weights (d(n)) satisfy some reasonable conditions and 0 ≤ σ ≤ 1/2. We use an approach based on methods of stochastic processes, in particular the metric entropy method developed in [8].
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 des Sciences Mathématiques
سال: 2014
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2013.12.002