The size of Wiman–Valiron discs for subharmonic functions of a certain type. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Fenton, P.C.; Lingham, E.F.
• Is Part Of: Complex variables and elliptic equations. Volume 61:Issue 4(2016)
• Page Start: 456
• Page End: 468
• Publication Date: 2016-04-02
• Subjects: subharmonic -- Wiman-Valiron; 31A05 (primary) -- 30B10 -- 30D30 -- 30D35(secondary); Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2015.1095186
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : Wiman–Valiron theory and the results of Macintyre about "flat regions" describe the asymptotic behaviour of entire functions in certain discs around maximum points. We use a technique of Bergweiler, Rippon and Stallard to describe the asymptotic behaviour of a certain type of subharmonic function, and a technique of Bergweiler to estimate the size of its Wiman–Valiron discs from above and below. The results are extended to -subharmonic functions.