On sums of roots of infinite order entire functions

Abstract

A class of infinite order entire functions is considered. Estimates for sums of the roots are derived. These estimates supplement the Hadamard theorem. Moreover, we establish a new estimate for the counting function of the roots, which in appropriate situations can be more useful than the Jensen inequality.

Keywords:

• Entire functions
• Estimates for zeros
• Hadamard theorem
• Counting function
• AMS 2000 Mathematics Subject Classifications: 30D20

Acknowledgements

This research was supported by Kamea fund of the Israel.

Notes

E-mail: [email protected]

Additional information

Notes on contributors

M.I. Gil *

E-mail: [email protected]