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Differentiation Evens out Zero Spacings
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2005 |
| Abstract | If f is a polynomial with all of its roots on the real line, then the roots of the derivative f ′ are more evenly spaced than the roots of f . The same holds for a real entire function of order 1 with all its zeros on a line. In particular, we show that if f is entire of order 1 and has sufficient regularity in its zero spacing, then under repeated differentiation the function approaches, after normalization, the cosine function. We also study polynomials with all their zeros on a circle, and we find a close analogy between the two situations. This sheds light on the spacing between zeros of the Riemann zeta-function and its connection to random matrix polynomials. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0310252v2.pdf |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/2005-357-09/S0002-9947-05-03721-9/S0002-9947-05-03721-9.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0310252v3.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0310252v1.pdf |
| Alternate Webpage(s) | http://math.stanford.edu/~rhoades/FILES/diffEvensOut.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Plant Roots Polynomial Spacing |
| Content Type | Text |
| Resource Type | Article |
