Finite groups and multiplicative \(\eta\)-products. (Russian. English summary) Zbl 1077.11033

Voskresenskaya, G. V.

Vestn. Samar. Gos. Univ., Mat. Mekh. Fiz. Khim. Biol. 2000, No. 2(16), 18-25 (2000).

Let \(\eta(z)\) denote the Dedekind eta function. D. Dummit, H. Kisilevsky and J. McKay [Contemp. Math. 45, 89–98 (1985; Zbl 0578.10028)] proved that some products of powers \(\eta^t(az),a,t \in \mathbb{N}\) are the special type parabolic forms.
The author studies the correspondence these cusp forms and elements of finite groups. The case of the cyclic groups and metacyclic groups with normal cyclic subgroups of order 9 and 18 are considered in details.

Reviewer: Guram Gogishvili (Tbilisi)

MSC:

11F22	Relationship to Lie algebras and finite simple groups
11F20	Dedekind eta function, Dedekind sums
11F11	Holomorphic modular forms of integral weight

Keywords:

Dedekind eta function; finite group; cusp form; cyclic group; metacyclic group

Citations:

Zbl 0578.10028