5

Part of 2002 SNSB Admission

Problems(1)

A complex condition for a function to be 0

Source: Admission to SNSB, 2002

f:\mathbb{D}\longrightarrow\mathbb{C}

be a continuous function, where

\mathbb{D}

is the closed unit disk. Suppose that

f

is holomorphic on the open unit disk and that

e^{i\theta }

are roots, for any

\theta\in\left[ 0,\pi /4 \right] .

f=0_{\mathbb{D}} .

functioncomplex analysis