$\cos \pi \lambda$ again
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- by P. C. Fenton PDF
- Proc. Amer. Math. Soc. 131 (2003), 1875-1880 Request permission
Abstract:
It is shown that if, for an entire function, \[ \liminf _{r\to \infty } \log M(r)/r^{\lambda } = 0 \] where $0< \lambda <1$, then \[ \limsup _{r\to \infty }(\log m(r)-\cos \pi \lambda \log M(r))/\log r = \infty . \] In the proof, the zeros of the function are redistributed to minimize the large values of $\log m(r) -\cos \pi \lambda \log M(r)$.References
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Additional Information
- P. C. Fenton
- Affiliation: Department of Mathematics, University of Otago, P.O. Box 56, Dunedin, New Zealand
- Received by editor(s): February 7, 2002
- Published electronically: November 6, 2002
- Communicated by: Juha M. Heinonen
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1875-1880
- MSC (2000): Primary 30D15
- DOI: https://doi.org/10.1090/S0002-9939-02-06750-3
- MathSciNet review: 1955276