Finiteness of simple holomorphic eta quotients of a given weight

Abstract

We provide a simplified proof of Zagier's conjecture / Mersmann's theorem which states that of any particular weight, there are only finitely many holomorphic eta quotients, none of which is an integral rescaling of another eta quotient or a product of two holomorphic eta quotients other than 1 and itself.

arXiv comment14 pages. arXiv admin note: text overlap with arXiv:1602.02835, arXiv:1602.03087, arXiv:1602.02814