Browsing by Subject "Maximum modulus point"
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Item Open Access Distance between a maximum point and the zero set of an entire function(2006) Üreyen, Adem ErsinWe obtain asymptotical bounds from below for the distance between a maximum modulus point and the zero set of an entire function. Known bounds (Macintyre, 1938) are more precise, but they are valid only for some maximum modulus points. Our bounds are valid for all maximum modulus points and moreover, up to a constant factor, they are unimprovable. We consider entire functions of regular growth and obtain better bounds for these functions. We separately study the functions which have very slow growth. We show that the growth of these functions can not be very regular and obtain precise bounds for their growth irregularity. Our bounds are expressed in terms of some smooth majorants of the growth function. These majorants are defined by using orders, types, (strong) proximate orders of entire functions.Item Open Access The distance between maximum modulus points and the zero set of an entire function(2001) Üreyen, Adem ErsinWe obtain asymptotical bounds from below for the distance between a maximum modulus point and the zero set of an entire function of finite order. Known bounds(Macintyre,1938) are more precise but they are valid only for some maximum modulus points and can not be valid for all of them. Our bounds are valid for each maximum modulus point and are precise in some sense. Our method is based on Macintyre's ideas and on the techniques of proxi mate and strong proximate orders. Keywords: Entire function, Maximum modulus point, Zero set, Proximate order, Strong proximate order.