[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2017.075

ON THE SHAPE OF MAXIMUM CURVE OF e^az²+bz+c

KIM, MIHWA (Department of Mathematics, Soongsil University)
KIM, JEONG-HEON (Department of Mathematics, Soongsil University)

Publication Information

Journal of applied mathematics & informatics / v.35, no.1_2, 2017 , pp. 75-82 More about this Journal

Abstract

In this paper, we investigate the proper shape and location of the maximum curve of transcendental entire functions $e^{az^2+bz+c}$ . We show that the alpha curve of $e^{az^2+bz+c}$ is a subset of a rectangular hyperbola, and the maximum curve is the connected set originating from the origin as a subset of the alpha curve.

Keywords

beta curve; alpha curve; maximum curve of an entire function;

Citations & Related Records

Reference

1	W.K. Haymann, A characterization of the maximal modulus of functions regular at the origin, J. Analyse Math 1, (1951), 135-154. DOI
2	A.I. Markushevich(trans. and ed. by R. A. Silvermann), Theory of Functions of a Complex Variable, Chelsea, New York, 1977.
3	T.F. Tyler, Maximum curves and isolated points of entire functions, Proc. Amer. Math. Soc. 128 no 9, (2000), 2561-2565. DOI

KSCI

ON THE SHAPE OF MAXIMUM CURVE OF eaz2+bz+c

ON THE SHAPE OF MAXIMUM CURVE OF e^az²+bz+c