## Turán’s problem 10 revisited (2008)

by
Johan Andersson

Citations: | 2 - 2 self |

### BibTeX

@MISC{Andersson08turán’sproblem,

author = {Johan Andersson},

title = {Turán’s problem 10 revisited},

year = {2008}

}

### OpenURL

### Abstract

In this paper we prove that inf max n∑ z ν k ∣ = √ n + O ( n 0.2625+ǫ). (ǫ> 0) |zk|≥1 ν=1,...,n2 k=1 This improves on the bound inf max n∑ |zk|≥1 ν=1,...,n2 z k=1 ν k ∣ ≤ √ 6n log(1 + n2) of Erdős and Renyi. In the special case of n + 1 being a prime we have previously obtained the much sharper result n ≤ inf max n∑ z ν k