翻转操作员和局部和的马斯形式
Kathrin Bringmann1, Andreas Mono2, Larry Rolen2
1Department of Mathematics and Computer Science, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany.
The Ramanujan journal
|August 11, 2025
概括
翻转运算符对局部和的马斯形式的作用类似于对和的马斯形式的作用. 这项研究扩大了对翻转操作员的理解.
科学领域:
- 数学理论 数学理论
- 自体形的形式 自体形的形式
背景情况:
- 可控增长的和马斯形式在数论中至关重要.
- 关键运算符包括Bol,影子和翻转运算符,每个运算符控制这些形式的特定方面.
- 马斯-波因卡雷序列为负重波马斯形式提供了基础.
研究的目的:
- 为了研究在局部和的马斯形式上翻转运算符的行为.
- 为了在这些形式上为翻转运算符建立一个类似的属性,就像在和的马斯形式中观察到的那样.
- 为了将翻转运算符的属性连接到不同类型的Maass形式中.
主要方法:
- 在和马斯形式的背景下分析差分运算符 (Bol,shadow,flipping).
- 马斯-波因卡雷序列作为负重波马斯形式的基础的研究.
- 将这些概念扩展到局部和的马斯形式,以及它们与高压类型的庞卡雷数列的关系.
主要成果:
- 翻转操作员对局部和的马斯形式的作用被证明与其对和的马斯形式的作用相似.
- 类似的属性被证明是用于曲类型的波因卡雷数列的翻转运算符.
- 这项研究证实了翻转运算符和这些先进的数理论对象之间的相互作用.
结论:
- 翻转操作员在操纵和和局部和马斯形式的组件方面发挥着一致的作用.
- 这项研究加深了对马斯形式理论中的结构和转变的理解.
- 这些发现有助于正在进行的研究Shimura和Shintani电梯和相关的自变形形式.
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