Zeros of sections of exponential sums
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2006
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| _version_ | 1866912080209117184 |
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| author | Bleher, Pavel Mallison jr, Robert |
| author_facet | Bleher, Pavel Mallison jr, Robert |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_ph_0605066 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | Zeros of sections of exponential sums Bleher, Pavel Mallison jr, Robert Mathematical Physics Classical Analysis and ODEs 30D20; 30E10 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. |
| title | Zeros of sections of exponential sums |
| topic | Mathematical Physics Classical Analysis and ODEs 30D20; 30E10 |
| url | https://arxiv.org/abs/math-ph/0605066 |