
JAMES HUARD, Department of Mathematics, Canisius College, Buffalo, New York 14208, USA 
An arithmetic reciprocity relation of Liouville type and applications 
Let n be a positive integer and let
be an even function. Liouville gave the identity
where the sum on the left hand side is taken over all positive
integers a, A, b, B satisfying
aA + bB =n. Some
generalizations of this identity will be presented and applications
will be made to the determination of such sums as