ON SOME TRIGONOMETRIC AND EXPONENTIAL LATTICE SUMS

Certain two-dimensional trigonometric lattice series, the ordinary con vergence of which involves unresolved questions of a deep and delicate number-theoretic nature, are shown to be summable by a special Abelia n method and their Abelian sums are obtained. This is done by first ev aluating an absolutely convergent exponential lattice series and then analytically extending its sum. (C) 1994 Academic Press, Inc.