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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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