Let a, a1, . . . , ad be positive integers, m1, . . . ,md nonnegative integers, and z1, . . . , zd complex numbers. We study expressions of the form ∑

In this paper, we define generalized Hardy-Berndt sums and elliptic analogue of the generalized Hardy-Berndt sums related to elliptic Bernoulli polynomials. We give relations between the Weierstrass ℘(z)-function, Hardy-Bernd sums, theta functions and generalized Dedekind eta function. 2000 Mathematical Subject Classification: Primary 11F20, 11B68; Secondary 14K25, 14H42.

We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it.