论文标题
关于序列作为恒定项的表示
On the representability of sequences as constant terms
论文作者
论文摘要
一个恒定的项序列是一系列有理数的序列，其$ n $ th的术语是$ p^n（\ boldsymbol {x}）q（\ boldsymbol {x}）$的恒定项，其中$ p（\ boldsymbol {x}）$和$ q（\ boldsymbol {x}）和$ q（\ boldsymbol {x}）$ polotyivarent poltyivarent lotivarent lotivarent larent lotiv larent larent larent larent larent larent larent larent larent larent larent larent larent。尽管此类序列的生成函数总是多元合理函数的对角线，因此特殊时期函数是由Don Zagier提出的一个著名的开放问题，以对对角线进行分类为恒定术语。在本文中，我们在满足恒定系数的线性复发的情况下提供了这样的分类。我们还考虑了高几何序列的情况，对于简单的说明性序列序列的属性，我们将序列分类为恒定术语。
A constant term sequence is a sequence of rational numbers whose $n$-th term is the constant term of $P^n(\boldsymbol{x}) Q(\boldsymbol{x})$, where $P(\boldsymbol{x})$ and $Q(\boldsymbol{x})$ are multivariate Laurent polynomials. While the generating functions of such sequences are invariably diagonals of multivariate rational functions, and hence special period functions, it is a famous open question, raised by Don Zagier, to classify diagonals that are constant terms. In this paper, we provide such a classification in the case of sequences satisfying linear recurrences with constant coefficients. We also consider the case of hypergeometric sequences and, for a simple illustrative family of hypergeometric sequences, classify those that are constant terms.
