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Eulerian series as Modular forms revisited


Author: Eric T. Mortenson
Journal: Proc. Amer. Math. Soc. 143 (2015), 2379-2385
MSC (2010): Primary 11B65, 11F11, 11F27
DOI: https://doi.org/10.1090/S0002-9939-2015-12451-3
Published electronically: February 4, 2015
MathSciNet review: 3326020
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Abstract: Recently, Bringmann, Ono, and Rhoades employed harmonic weak Maass forms to prove results on Eulerian series as modular forms. By changing the setting to Appell-Lerch sums, we shorten the proof of one of their main theorems. In addition we discuss connections to recent work of Kang.


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Additional Information

Eric T. Mortenson
Affiliation: Max-Planck-Institut für Mathematik, Vitvatsgasse 7, 53111 Bonn, Germany
Email: etmortenson@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12451-3
Keywords: Appell--Lerch sums, Eulerian forms, $q$-hypergeometric series
Received by editor(s): September 23, 2013
Received by editor(s) in revised form: January 21, 2014, and January 23, 2014
Published electronically: February 4, 2015
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2015 American Mathematical Society