On the zeros of the derivative of a rational function
β Scribed by A.W Goodman
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 236 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
We extend some results of Giroux and Rahman (Trans. Amer. Math. Soc. 193 (1974), 67 98) for Bernstein-type inequalities on the unit circle for polynomials with a prescribed zero at z=1 to those for rational functions. These results improve the Bernstein-type inequalities for rational functions. The
Let k be any positive integer and N 0, k (T ) the number of the zeros in the interval (0, T ) of Z (k) (t), the kth derivative of Hardy's Z-function. We prove an inequality for N 0, k (T) (Theorem 1), and also prove that it can be replaced by the equality under the Riemann hypothesis (Theorem 2). Th