Infinite products over visible lattice points. (English) Zbl 0811.05006

Campbell, Geoffrey B.

Int. J. Math. Math. Sci. 17, No. 4, 637-654 (1994).

The concept of visible-from-the-origin lattice points in the \(xy\) plane has been described in Apostol. These points have the property that their coordinates are relatively prime. Recently a number of new identities based on summation or products taken on these points have been obtained by the author. In this paper some of the more notable results are presented. These are extended to higher dimensions and more general theorems are proved.

Reviewer: M.Cheema (Tucson)

MSC:

05A19	Combinatorial identities, bijective combinatorics
11P21	Lattice points in specified regions
11M06	\(\zeta (s)\) and \(L(s, \chi)\)
30B50	Dirichlet series, exponential series and other series in one complex variable

Keywords:

visible lattice points; infinite products; identities