K. Seip

activity

19922023

most citedThe Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive

204 citations · 749 across the 51 of their papers we have counts for

collaborators

Showing 2014 · math.NTShow all

3 papers · 2 filters

math.NT2014★ 23 cited

Helson's problem for sums of a random multiplicative function

Andriy Bondarenko, Kristian Seip

We consider the random functions $S_{N} (z) := \sum_{n = 1}^{N} z (n)$ , where $z (n)$ is the completely multiplicative random function generated by independent Steinhaus variables $z (p)$ . It…

math.NT2014★ 26 cited

An inequality of Hardy--Littlewood type for Dirichlet polynomials

Andriy Bondarenko, Winston Heap, Kristian Seip

The $L^{q}$ norm of a Dirichlet polynomial $F (s) = \sum_{n = 1}^{N} a_{n} n^{- s}$ is defined as \[\| F\|_q:=(\lim_{T\to\infty}\frac{1}{T}\int_{0}^T |F(it)|^qdt)^{1/q}\] for $0 < q < \infty$ . I…

math.NT2014★ 22 cited

GCD sums and complete sets of square-free numbers

Andriy Bondarenko, Kristian Seip

It is proved that \[ \sum_{k,{\ell}=1}^N\frac{\gcd(n_k,n_{\ell})}{\sqrt{n_k n_{\ell}}} \ll N\exp\left(C\sqrt{\frac{\log N \log\log\log N}{\log\log N}}\right) \] holds for arbitrary…