论文标题
涉及无限产品的Hecke型系列
Hecke-type series involving infinite products
论文作者
论文摘要
自Jacobi和Hecke的研究以来，Hecke型系列已受到广泛关注。特别是，涉及无限产品的Hecke型系列引起了许多数学家的广泛兴趣，包括KAC，Peterson，Andrews，Bressoud和Liu。在这些人的作品的激励下，我们研究了涉及无限产品的Hecke型系列。特别是，我们建立了一些涉及无限产物的Hecke型系列，然后获得这些系列的截断版本以及其他类型的其他已知系列。结果，还提出了三个针对某些分区功能的不平等家庭。我们的证明在很大程度上依赖于刘的作品中的公式。
Since the study by Jacobi and Hecke, Hecke-type series have received extensive attention. Especially, Hecke-type series involving infinite products have attracted broad interest among many mathematicians including Kac, Peterson, Andrews, Bressoud and Liu. Motivated by the works of these people, we study Hecke-type series involving infinite products. In particular, we establish some Hecke-type series involving infinite products and then obtain the truncated versions of these series as well as some other known series of the same type. As consequences, three families of inequalities for certain partition functions are also presented. Our proofs heavily rely on a formula from the work of Zhi-Guo Liu.
