Counting Eta-Quotients of Prime Level
Number Theory
2018-04-11 v1
Abstract
It is known that all modular forms on SL_2(Z) can be expressed as a rational function in eta(z), eta(2z) and eta(4z). By utilizing known theorems, and calculating the order of vanishing, we can compute the eta-quotients for a given level. Using this count, knowing how many eta-quotients are linearly independent and using the dimension formula, we can figure out a subspace spanned by the eta-quotients. In this paper, we primarily focus on the case where N=p a prime.
Cite
@article{arxiv.1611.08969,
title = {Counting Eta-Quotients of Prime Level},
author = {Allison Arnold-Roksandich and Kevin James and Rodney Keaton},
journal= {arXiv preprint arXiv:1611.08969},
year = {2018}
}
Comments
13 pages, 3 tables, REU results