Finiteness of simple holomorphic eta quotients of a given weight

2016/02/09 by Soumya Bhattacharya, Bhattacharya, Soumya · 1 citation
Mathematics · #11F11 (Primary) #11F12 (Secondary) #11F20 #11F37 #11G16 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F12 #msc:11F20 #msc:11F37 #msc:11G16

paper · pdf · doi:10.48550/arxiv.1602.02825

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

arxiv created 2016/07/08 · arxiv updated 2016/07/11

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.

Citations

• Holomorphic eta quotients of weight 1/2
• Irreducibility of a holomorphic eta quotient is determinable
• Finiteness of irreducible holomorphic eta quotients of a given level

Cited by

• Holomorphic eta quotients of weight 1/2

Related

• Finiteness of irreducible holomorphic eta quotients of a given level
• Holomorphic eta quotients of weight 1/2
• Infinite Families of Simple Holomorphic Eta Quotients
• Irreducibility of a holomorphic eta quotient is determinable
• Vanishing properties of Fourier coefficients of holomorphic η-quotients