论文标题
某些用于限制$ q $产品系数的公式
Some formulae for coefficients in restricted $q$-products
论文作者
论文摘要
在本文中，我们得出了一些涉及多项式系数的公式，这些公式在限制分区的研究中很自然。我们的方法涉及Li and Wan（Sci。Chine。Math。2010）的最近发现的筛技术。基于这种方法，通过考虑不同阶的循环基团，我们为这些系数获得了一些新的结果。 $ \ mathbb {z} _ {n} $中的任何组的一般结果都保留，其中$ n \ in \ mathbb {n} $中，并根据涉及统一根源的表达式表示某些系数的偏额。通过将$ n $用于不同的值，我们看到这些表达式在某些情况下简化了，并且获得了涉及这些系数的几个不错的身份。我们还使用Sudler的结果（QJMAAT 1964）获得了这些系数最大绝对值的渐近公式。
In this paper, we derive some formulae involving coefficients of polynomials which occur quite naturally in the study of restricted partitions. Our method involves a recently discovered sieve technique by Li and Wan (Sci. China. Math. 2010). Based on this method, by considering cyclic groups of different orders we obtain some new results for these coefficients. The general result holds for any group of the form $\mathbb{Z}_{N}$ where $N\in\mathbb{N}$ and expresses certain partial sums of coefficients in terms of expressions involving roots of unity. By specializing $N$ to different values, we see that these expressions simplify in some cases and we obtain several nice identities involving these coefficients. We also use a result of Sudler (QJMAAT 1964) to obtain an asymptotic formula for the maximum absolute value of these coefficients.
