  The aim of the present paper is to obtain the sharp bounds of the Hankel
determinants H_2(3) and H_3(1) for the well known class SL^* of starlike
functions associated with the right lemniscate of Bernoulli. Further for n=3,
we find the sharp bound of the Zalcman functional for the class SL^*. In
addition, a couple of interesting results of SL^* is appended at the end.
