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Mathematics > Number Theory

arXiv:1812.08698 (math)
[Submitted on 20 Dec 2018 (v1), last revised 2 Oct 2019 (this version, v2)]

Title:Theta block conjecture for paramodular forms of weight 2

Authors:Valery Gritsenko, Haowu Wang
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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 only known infinite series of theta-blocks of weight $2$ and $q$-order $1$. We also consider some applications of this result.
Comments: Minor revision, accepted for publication in Proc. Amer. Math. Soc
Subjects: Number Theory (math.NT)
MSC classes: 11F30, 11F46, 11F50, 11F55, 14K25
Cite as: arXiv:1812.08698 [math.NT]
  (or arXiv:1812.08698v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1812.08698

Submission history

From: Haowu Wang [view email]
[v1] Thu, 20 Dec 2018 17:02:39 UTC (17 KB)
[v2] Wed, 2 Oct 2019 15:30:17 UTC (18 KB)
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