Automorphic products of singular weight for simple lattices

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• 作者：Moritz Dittmann (1)
  Heike Hagemeier (2)
  Markus Schwagenscheidt (1)
  
  1. Fachbereich Mathematik ; Technische Universit盲t Darmstadt ; 64289 ; Darmstadt ; Germany
  2. Bundesamt f眉r Sicherheit in der Informationstechnik ; Postfach 200363 ; 53133 ; Bonn ; Germany
  
• 关键词：Automorphic forms ; Theta correspondence ; Simple lattices
• 刊名：Mathematische Zeitschrift
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：279
• 期：1-2
• 页码：585-603
• 全文大小：237 KB
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  10. Hagemeier, H.: Automorphe Produkte singul盲ren Gewichts. PhD thesis (2010).
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  14. Scheithauer, N.R.: The Weil representation of \(\text{ SL }_{2}({\mathbb{Z}})\) and some applications. Int. Math. Res. Not. 2009(8), 1488鈥?545 (2009)
  15. Scheithauer, N.R.: Some constructions of modular forms for the Weil representation of \(\text{ SL }_{2}({\mathbb{Z}})\) . Nagoya Math. J. (to appear)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1823

文摘

We classify the simple even lattices of square free level and signature \((2,n), n \ge 4\) . A lattice is called simple if the space of cusp forms of weight \(1+n/2\) for the dual Weil representation of the lattice is trivial. For a simple lattice every formal principal part obeying obvious conditions is the principal part of a vector valued modular form. Using this, we determine all holomorphic Borcherds products of singular weight (arising from vector valued modular forms with non-negative principal part) for the simple lattices. We construct the corresponding vector valued modular forms by eta products and compute expansions of the automorphic products at different cusps.