Bounds for orders of zeros of a class of Eisenstein series and their applications on dual pairs of eta quotients
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- by Amir Akbary and Zafer Selcuk Aygin
- Proc. Amer. Math. Soc. 151 (2023), 4565-4578
- DOI: https://doi.org/10.1090/proc/16533
- Published electronically: August 4, 2023
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Abstract:
Let $k$ be an even positive integer, $p$ be a prime and $m$ be a nonnegative integer. We find an upper bound for orders of zeros (at cusps) of a linear combination of classical Eisenstein series of weight $k$ and level $p^m$. As an immediate consequence we find the set of all eta quotients that are linear combinations of these Eisenstein series and hence the set of all eta quotients of level $p^m$ whose derivatives are also eta quotients.References
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Bibliographic Information
- Amir Akbary
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada
- MR Author ID: 650700
- Email: amir.akbary@uleth.ca
- Zafer Selcuk Aygin
- Affiliation: Science Department, Northwestern Polytechnic, Grande Prairie, AB T8V 4C4, Canada
- MR Author ID: 1134845
- ORCID: 0000-0001-5329-1663
- Email: selcukaygin@gmail.com
- Received by editor(s): August 6, 2022
- Received by editor(s) in revised form: December 13, 2022, and January 17, 2023
- Published electronically: August 4, 2023
- Additional Notes: The first author was partially supported by NSERC. The second author was partially supported by a PIMS postdoctoral fellowship.
- Communicated by: Amanda Folsom
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4565-4578
- MSC (2020): Primary 11F11, 11F20, 11F27
- DOI: https://doi.org/10.1090/proc/16533
- MathSciNet review: 4634864