Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2006
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/math-ph/0605066 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We derive the large $n$ asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the $n$-th section of the exponential sum into ``genuine zeros'', which approach, as $n\to\infty$, the zeros of the exponential sum, and ``spurious zeros'', which go to infinity as $n\to\infty$. We show that the spurious zeros, after scaling down by the factor of $n$, approach a ``rosette'', a finite collection of curves on the complex plane, resembling the rosette. We derive also the large $n$ asymptotics of the ``transitional zeros'', the intermediate zeros between genuine and spurious ones. Our results give an extension to the classical results of Szegö about the large $n$ asymptotics of zeros of sections of the exponential, sine, and cosine functions.