Secord-order cusp forms and mixed mock modular forms

被引：0
作者：
Kathrin Bringmann
Ben Kane
机构：
[1] University of Cologne,Mathematical Institute
来源：
The Ramanujan Journal | 2013年 / 31卷
关键词：
Modular forms; Second-order modular forms; Mixed mock modular forms; Poincaré series; Harmonic Maass forms; 11F11; 11F12; 11F37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the space of second order cusp forms. We determine that this space is precisely the same as a certain subspace of mixed mock modular forms. Based upon Poincaré series of Diamantis and O’Sullivan (Trans. Am. Math. Soc. 360:5629–5666, 2008) which span the space of second order cusp forms, we construct Poincaré series which span a natural (more general) subspace of mixed mock modular forms.
引用
收藏
页码：147 / 161
页数：14
相关论文
共 52 条
  • [1] Andrews G.(1966)On the theorems of Watson and Dragonette for Ramanujan’s mock theta functions Am. J. Math. 88 454-490
  • [2] Andrews G.(2007)Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks Invent. Math. 169 37-73
  • [3] Borcherds R.(1992)Monstrous moonshine and monstrous Lie superalgebras Invent. Math. 109 405-444
  • [4] Bringmann K.(2008)On the explicit construction of higher deformations of partition statistics Duke Math. J. 144 195-233
  • [5] Bringmann K.(2009)Partition statistics and quasiharmonic maass forms Int. Math. Res. Not. 2009 63-97
  • [6] Garvan F.(2011)An extension of the Hardy–Ramanujan circle method and applications to partitions without sequences Am. J. Math. 133 1151-1178
  • [7] Mahlburg K.(2006)The Invent. Math. 165 243-266
  • [8] Bringmann K.(2007)( Math. Ann. 337 591-612
  • [9] Mahlburg K.(2010)) mock theta function conjecture and partition ranks Ann. Math. 171 419-449
  • [10] Bringmann K.(2009)Arithmetic properties of coefficients of half-integral weight Maass–Poincaré series Math. Ann. 345 547-558
123456