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2018 Counting eta-quotients of prime level
Allison Arnold-Roksandich, Kevin James, Rodney Keaton
Involve 11(5): 827-844 (2018). DOI: 10.2140/involve.2018.11.827

Abstract

It is known that a modular form on SL2() can be expressed as a rational function in η(z), η(2z) and η(4z). By using 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 the level is N=p, a prime. In this case, we will show an explicit count for the number of eta-quotients of level p and show that they are linearly independent.

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Allison Arnold-Roksandich. Kevin James. Rodney Keaton. "Counting eta-quotients of prime level." Involve 11 (5) 827 - 844, 2018. https://doi.org/10.2140/involve.2018.11.827

Information

Received: 18 December 2016; Revised: 30 July 2017; Accepted: 24 August 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06866586
MathSciNet: MR3784029
Digital Object Identifier: 10.2140/involve.2018.11.827

Subjects:
Primary: 11F11, 11F20, 11F37

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2018
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