A GENERALIZATION OF MENON-RAO-SURY'S IDENTITIES TO ADDITIVE CHARACTERS BY TÓTH'S METHOD.

In this paper, we obtain a new Menon-type identity:... where λj(b) := exp(2πiwjb/n) is an additive character of Z/nZ for 1 ⩽ j ⩽ r, (c1, . . .,cs) ∈ Zs is a fixed vector such that gcd(c1, . . .,cs,n) = 1, ϕs(n) = nsΠp|n(1- p-s) is the Jordan's totient function and σr(n) = Σd|n dr is the rth divisor function. This extends Rao's identity ([9]) and Sury's identity ([11]) to additive characters. Following the method of T'oth [14], we also generalize the above identity to arbitrary arithmetic function. [ABSTRACT FROM AUTHOR]