VPW: Visiting Professorships for Women: Theta Series and Automorphic Forms

VPW：女性客座教授职位：Theta 系列和自同构形式

• 批准号: 9627069
• 负责人: Lynne Walling
• 金额: $ 10.29万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1999-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9627069&HistoricalAwards=false
• 关键词: VPW; Visiting; Professorships; Women; Theta

In recent work, Dr. Lynne Walling developed an algebraic proof of Siegel's representation formula, yielding formulas more explicit than those of Siegel to describe average representation numbers of positive definite quadratic forms of even rank and odd level. She is currently working with J.L. Hafner, using the theory of automorphic forms to extend these results to indefinite quadratic forms, obtaining explicit formulas for the measures of the representations of the indefinite forms over number fields and over function fields. In work with O. Imamoglu, Dr. Walling has defined a symplectic theta function over a function field and computed the transformation formula nd will develop some theory of Siegel modular forms and Jacobi forms in the function field setting. Information will be gained regarding representations of quadratic forms by higher dimensional quadratic forms. She also intends to extend the techniques developed in work with J. Hoffstein and K.D. Merrill, explicitly computing the Fourier coefficients of cusp forms of weights 0 and 1/2 for congruence subgroups that admit only one-dimensional spaces of cusp forms. Interactive activities include developing curricula for college/university mathematics courses based on contemplation, precise reasoning and clear communication; developing a summer research institute for women mathematicians; and running a one-week conference for women in harmonic analysis and number theory.

在最近的工作中，Lynne Walling博士对Siegel的表示公式进行了代数证明，得到了比Siegel更明确的公式来描述偶数秩和奇数水平的正定二次型的平均表示数。 目前，她与J. L。Hafner利用自守形式的理论将这些结果推广到不定二次型，得到了数域和函数域上不定二次型的表示的测度的显式公式。 与O。Imamoglu，Walling博士定义了函数域上的辛theta函数，并计算了变换公式，并将在函数域设置中发展Siegel模形式和Jacobi形式的一些理论。 信息将获得关于表示二次形式的高维二次形式。 她还打算扩展与J. Hoffstein和K.D. 梅里尔，明确计算权为0和1/2的尖点形式的傅立叶系数的同余子群，只允许一维空间的尖点形式。 互动活动包括：根据沉思、精确推理和明确交流为大专/大学数学课程编制课程;为女数学家设立一个暑期研究所;为妇女举办一个为期一周的调和分析和数论会议。