• Corpus ID: 19025937

Differentiating polynomials, and zeta(2)

@article{Farmer2008DifferentiatingPA,
  title={Differentiating polynomials, and zeta(2)},
  author={David W. Farmer and Robert C. Rhoades},
  journal={arXiv: General Mathematics},
  year={2008}
}
We study the derivatives of polynomials with equally spaced zeros and find connections to the values of the Riemann zeta-function at the positive even integers. 

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References

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TLDR
A modest improvement of the theorem obtained by taking into account the multiplicities of the zeros of the polynomial by stating the original theorem as it appears in Gideon Peyser's theorem.
Differentiation evens out zero spacings
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