Finiteness of irreducible holomorphic eta quotients of a given level

Authors

Soumya Bhattacharya, Bruno Kessler Foundation

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

We show that for any positive integer N, there are only finitely many holomorphic eta quotients of level N, none of which is a product of two holomorphic eta quotients other than 1 and itself. This result is an analog of Zagier’s conjecture/Mersmann’s theorem which states that of any given weight, there are only finitely many irreducible holomorphic eta quotients, none of which is an integral rescaling of another eta quotient. We construct such eta quotients for all cubefree levels. In particular, our construction demonstrates the existence of irreducible holomorphic eta quotients of arbitrarily large weights.

First Page

423

Last Page

443

DOI

10.1007/s11139-017-9982-6

Publication Date

2-15-2019

Comments

Open Access, Green

Recommended Citation

Bhattacharya, Soumya, "Finiteness of irreducible holomorphic eta quotients of a given level" (2019). Journal Articles. 947.
https://digitalcommons.isical.ac.in/journal-articles/947