Zeros of successive derivates of a class of real entire functions of exponential type
HTML articles powered by AMS MathViewer
- by Li-Chien Shen PDF
- Proc. Amer. Math. Soc. 100 (1987), 627-634 Request permission
Abstract:
Using the method of steepest descent we prove that for a class of real entire functions of exponential type $\tau$ the spacings of the adjacent zeros of ${f^{(n)}}$ converge to $\pi \tau /2$.References
- Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
- R. P. Boas Jr. and Carl L. Prather, Final sets for operators on finite Fourier transforms, Houston J. Math. 5 (1979), no. 1, 29–36. MR 533636
- W. K. Hayman, A generalisation of Stirling’s formula, J. Reine Angew. Math. 196 (1956), 67–95. MR 80749, DOI 10.1515/crll.1956.196.67
- G. Polya, On the zeros of the derivatives of a function and its analytic character, Bull. Amer. Math. Soc. 49 (1943), 178–191. MR 7781, DOI 10.1090/S0002-9904-1943-07853-6
- C. L. Prather, Final sets for operators on real entire functions of order one, normal type, Proc. Amer. Math. Soc. 90 (1984), no. 3, 363–369. MR 728349, DOI 10.1090/S0002-9939-1984-0728349-4
- Murali Rao and Li-Chien Shen, On the final set of a real entire function of exponential type, Proc. Amer. Math. Soc. 99 (1987), no. 4, 700–704. MR 877043, DOI 10.1090/S0002-9939-1987-0877043-0
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 627-634
- MSC: Primary 30D20; Secondary 30C15
- DOI: https://doi.org/10.1090/S0002-9939-1987-0894428-7
- MathSciNet review: 894428