Zerofree region for exponenetial sums

Details Zerofree region for exponenetial sums Zerofree region for exponenetial sums

2011-06-16

arxiv.org/abs/1106.3280v1

Mathematics

Number Theory

Scientific paper

We consider the following two closed sets in $C^n$. One is the diagonal D given by $ (z, z, z,...z_)$. The other is $A = \{(z_1,z_2,z_3,...z_n):.$ $.e^{z_1} + e^{z_2} +e^{z_3} +...+ e^{z_n}=0\}$. Clearly $D \cap A$ is empty. One can ask what is the distance between them. In this connection, Stolarsky [1] proved that the distance $d$ is given by $d^2 = (\log \ n)^2 + O (1)$. Some simple calculations will make one believe that the point $(k, 0, 0,..0)$ with $k = \log \ (n-1) + \pi i$ which lies on $A$ is one of the closest point to the diagaonal. We prove that this is indeed the case, atleast for sufficiently large $n$. This gives $d^2 = |k|^2 (1-1/n)$.

Affiliated with

Also associated with

No associations

Rating

Zerofree region for exponenetial sums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Zerofree region for exponenetial sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Zerofree region for exponenetial sums will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190450