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Interlacing of zeros of weakly holomorphic modular forms


Authors: Paul Jenkins and Kyle Pratt
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 63-77
MSC (2010): Primary 11F11, 11F03
DOI: https://doi.org/10.1090/S2330-1511-2014-00010-9
Published electronically: May 28, 2014
MathSciNet review: 3211795
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Abstract: We prove that the zeros of a family of extremal modular forms interlace, settling a question of Nozaki. Additionally, we show that the zeros of almost all forms in a basis for the space of weakly holomorphic modular forms of weight $ k$ for $ \mathrm {SL}_2(\mathbb{Z})$ interlace on most of the lower boundary of the fundamental domain.


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Additional Information

Paul Jenkins
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: jenkins@math.byu.edu

Kyle Pratt
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: kvpratt@gmail.com

DOI: https://doi.org/10.1090/S2330-1511-2014-00010-9
Received by editor(s): September 4, 2013
Published electronically: May 28, 2014
Communicated by: Ken Ono
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)

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