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Counting
eta-quotients of prime level
Allison Arnold-Roksandich, Kevin James and Rodney Keaton
Vol. 11 (2018), No. 5, 827–844
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Abstract |
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It is known that a modular form on can be expressed as a rational function in , and . 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 , a prime. In this case, we will show an explicit count for the number of eta-quotients of level and show that they are linearly independent. |
Keywords
modular forms, eta-quotients, Dedekind eta-function, number
theory
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Mathematical Subject Classification 2010
Primary: 11F11, 11F20, 11F37
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Milestones
Received: 18 December 2016
Revised: 30 July 2017
Accepted: 24 August 2017
Published: 2 April 2018
Communicated by Kenneth S. Berenhaut
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Authors |
| Allison Arnold-Roksandich | |
| Department of Mathematics Oregon State University Corvallis, OR United States |
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| Kevin James | |
| Department of Mathematical
Sciences Clemson University Clemson, SC United States |
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| Rodney Keaton | |
| Department of Mathematics and
Statistics East Tennessee State University Johnson City, TN United States |
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