与θ级数相关的一般系数消失结果

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-08-01 DOI:10.1016/j.aam.2024.102742

Shane Chern , Dazhao Tang

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引用次数: 0

摘要

与θ级数相关的一些零星系数消失结果暗示了某些基本模式。通过将 Theta 幂扩展为 Theta 函数乘积的线性组合，我们提出了两种统一处理的策略。我们的方法依赖于研究两个θ级数的乘积在胡芬算子作用下的行为。为此，我们给出了一些明确的标准。我们不仅可以利用所提出的方法验证实验中发现的系数消失结果，还可以利用这些方法产生一系列普遍现象。

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General coefficient-vanishing results associated with theta series

There are a number of sporadic coefficient-vanishing results associated with theta series, which suggest certain underlying patterns. By expanding theta powers as linear combinations of products of theta functions, we present two strategies that will provide a unified treatment. Our approaches rely on studying the behavior of products of two theta series under the action of the huffing operator. For this purpose, some explicit criteria are given. We may use the presented methods to not only verify experimentally discovered coefficient-vanishing results, but also to produce a series of general phenomena.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.