Theta block conjecture for paramodular forms of weight 2
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- by Valery Gritsenko and Haowu Wang PDF
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Abstract:
In this paper we construct an infinite family of paramodular forms of weight $2$ which are simultaneously Borcherds products and additive Jacobi lifts. This proves an important part of the theta block conjecture of Gritsenko–Poor–Yuen (2013) related to the most important infinite series of theta blocks of weight $2$ and $q$-order $1$. We also consider some applications of this result.References
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Additional Information
- Valery Gritsenko
- Affiliation: Laboratoire Paul Painlevé, Université de Lille, 59655 Villeneuve d’Ascq Cedex, France; and National Research University Higher School of Economics, Russian Federation Laboratory of Mirror Symmetry, NRU HSE, 6 Usacheva str., Moscow, Russia, 119048
- MR Author ID: 219176
- Email: Valery.Gritsenko@univ-lille.fr
- Haowu Wang
- Affiliation: Laboratoire Paul Painlevé, Université de Lille, 59655 Villeneuve d’Ascq Cedex, France
- Address at time of publication: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
- MR Author ID: 1247984
- Email: haowu.wangmath@gmail.com
- Received by editor(s): January 29, 2019
- Received by editor(s) in revised form: September 7, 2019
- Published electronically: January 13, 2020
- Additional Notes: The first author was supported by the Laboratory of Mirror Symmetry NRU HSE (RF government grant, ag. N 14.641.31.0001) and IUF
The second author was supported by the Labex CEMPI (ANR-11-LABX-0007-01) of the University of Lille
The second author is the corresponding author - Communicated by: Amanda Folsom
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1863-1878
- MSC (2010): Primary 11F30, 11F46, 11F50, 11F55, 14K25
- DOI: https://doi.org/10.1090/proc/14876
- MathSciNet review: 4078073