论文标题
与确定的二次形式相关的Hecke型身份
Hecke-type identities associated with definite quadratic forms
论文作者
论文摘要
自Jacobi和Hecke的研究以来，Hecke Type系列引起了很多关注。与与不确定二次形式相关的此类系列不同，与确定的二次形式相关的Hecke型序列的身份在文献中很少见。在刘的作品的激励下，我们首先通过使用不同的$ q $转换公式来建立许多参数化的身份，并通过两个参数建立，然后通过专门选择这两个参数的选择来推断与确定的二次形式相关的各种Hecke-type身份。作为应用程序，我们利用其中一些Hecke型身份来建立多种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一些公式。
Since the study by Jacobi and Hecke, Hecke-type series have received a lot of attention. Unlike such series associated with indefinite quadratic forms, identities on Hecke-type series associated with definite quadratic forms are quite rare in the literature. Motivated by the works of Liu, we first establish many parameterized identities with two parameters by employing different $q$-transformation formulas and then deduce various Hecke-type identities associated with definite quadratic forms by specializing the choice of these two parameters. As applications, we utilize some of these Hecke-type identities to establish families of inequalities for several partition functions. Our proofs heavily rely on some formulas from the work of Zhi-Guo Liu.
