Linear relations among Poincaré series via harmonic weak Maass forms

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• 作者：Robert C. Rhoades (1)
  
• 关键词：Poincaré series ; Harmonic Maass forms ; Mock theta functions ; 11F37 ; 11F25 ; 11F30
• 刊名：The Ramanujan Journal
• 出版年：2012
• 出版时间：3 - December 2012
• 年：2012
• 卷：29
• 期：1
• 页码：311-320
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• 作者单位：Robert C. Rhoades (1)
  
  1. Department of Mathematics, Stanford University, Bldg 380, Stanford, CA, 94305, USA
  
• ISSN：1572-9303

文摘

We discuss the problem of the vanishing of Poincaré series. This problem is known to be related to the existence of weakly holomorphic forms with prescribed principal part. The obstruction to the existence is related to the pseudomodularity of Ramanujan’s mock theta functions. We embed the space of weakly holomorphic modular forms into the larger space of harmonic weak Maass forms. From this perspective we discuss the linear relations between Poincaré series.