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Theta block conjecture for paramodular forms of weight 2


Authors: Valery Gritsenko and Haowu Wang
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
Published electronically: January 13, 2020
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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.


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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
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
Email: haowu.wangmath@gmail.com

DOI: https://doi.org/10.1090/proc/14876
Keywords: Borcherds product, Gritsenko lift, paramodular forms, Jacobi forms
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
Article copyright: © Copyright 2020 American Mathematical Society