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In this note we find the maximal values of several symmetric functions in the variables which are the squares of distances |zi − z j| , 1 i < j d , between some d complex points z1, . . . ,zd in the unit disc. We compute the maximums of σm , for m = 1,2,3,4 , explicitly and find the conditions on z1, . . . ,zd under which those maximal values are attained. This problem is motivated by an inequality of Cassels (1966) and a subsequent conjecture of Alexander. Mathematics subject classification (2010): 52A40, 11R06.

Maximal values of symmetric functions in distances between points