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Sbornik: Mathematics, 2019, Volume 210, Issue 12, Pages 1702–1723
DOI: https://doi.org/10.1070/SM9241 (Mi sm9241) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Antisymmetric paramodular forms of weight 3

V. A. Gritsenkoab, H. Wanga

a Laboratoire Paul Painlevé, Université de Lille, Villeneuve d’Ascq, France
b National Research University Higher School of Economics, Moscow, Russia
English version PDF (608 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM9241
Abstract: The problem of the construction of antisymmetric paramodular forms of canonical weight 3 has been open since 1996. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer surfaces associated to $(1,t)$-polarised abelian surfaces. In this paper, we construct the first infinite family of antisymmetric paramodular forms of weight $3$ as automorphic Borcherds products whose first Fourier-Jacobi coefficient is a theta block.
Bibliography: 32 titles.
Keywords: Siegel modular forms, automorphic Borcherds products, theta functions and Jacobi forms, moduli space of abelian and Kummer surfaces, affine Lie algebras and hyperbolic Lie algebras.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
Labex ANR-11- LABX-0007-01
V. A. Gritsenko was supported by the Laboratory of Mirror Symmetry, NRU HSE, RF government grant, agreement no. 14.641.31.0001. H. Wang was supported by the Laboratory of Mirror Symmetry, NRU HSE, RF government grant, agreement no. 14.641.31.0001, and by Labex CEMPI, Université de Lillé (grant no. ANR-11-LABX-0007-01).
Received: 20.02.2019 and 10.07.2019
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 12, Pages 43–66
DOI: https://doi.org/10.4213/sm9241
Bibliographic databases:
Document Type: Article
UDC: 515.178.5+512.774.5+512.818.4
MSC: 11F27, 11F30, 11F46, 11F50, 11F55, 14K25
Language: English
Original paper language: Russian
Citation: V. A. Gritsenko, H. Wang, “Antisymmetric paramodular forms of weight 3”, Mat. Sb., 210:12 (2019), 43–66; Sb. Math., 210:12 (2019), 1702–1723
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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