Interlacing of zeros of weakly holomorphic modular forms
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- by Paul Jenkins and Kyle Pratt HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 63-77
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.References
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Additional Information
- Paul Jenkins
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- MR Author ID: 713798
- Email: jenkins@math.byu.edu
- Kyle Pratt
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- MR Author ID: 1015689
- Email: kvpratt@gmail.com
- Received by editor(s): September 4, 2013
- Published electronically: May 28, 2014
- Communicated by: Ken Ono
- © Copyright 2014 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- 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
- MathSciNet review: 3211795