ABSTRACT
In this chapter, the authors provide Λ-lattice point Hardy–Landau identities for the spherical context and constant lattice point weights. Basic discrepancy asymptotics are recapitulated. In fact, the authors work starts with an extension of the classical 2D Hardy–Landau identity for arbitrary lattices, however, in a way different from the traditional procedures known from analytic number theory. Instead, they exclusively base their verification on tools of the theory of Bessel functions as proposed by C. Muller for the bivariate case. The author discusses integral mean asymptotics for the Eeuler–green function. It deals with the basic version of a Hardy–Landau-type identity. In a certain sense, all investigations involving the number theoretical study of the classical 2D Hardy–Landau identity, which have been done during the past century, are based on (partial sums of) the “discrepancy replacement series”.
