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arXiv:1611.08969 [math.NT]AbstractReferencesReviewsResources

Counting Eta-Quotients of Prime Level

Allison Arnold-Roksandich, Kevin James, Rodney Keaton

Published 2016-11-28Version 1

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.

Comments: 13 pages, 3 tables, REU results
Categories: math.NT
Subjects: 11F20, 11F11, 11F37
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