The Restriction of Octonionic Theta Constants to the Quaternionic Half-Space

Theta functions on tube domains

“…Proof. Periodicity (Θ3) follows immediatly from the defining equation (3). It remains to prove that L is discrete.…”

“…(a) More generally, some authors also discuss partial involutions, thus j is assumed involutory but may have non-isolated fixed points; see e.g. Krieg [11], Dieckmann [2], Dieckmann and Krieg [3]. For the case of quaternion half spaces, all partial involutions were determined in [11], Ch.…”