Evaluation of L-series and Explorations in Mathematics

小行星9700542 该奖项资助围绕数论和计算数学领域的研究和教育计划。 在数论中，研究者将讨论几个关于算术感兴趣的L-级数的各种家庭的平均值的杰出的命题，包括n方面的Lindelof假设的“平均”版本;关于元形式的Whittaker-Fourier系数的猜想;以及关于经典的“两个立方体之和”椭圆曲线家庭的L-级数的平均值的猜想。研究人员希望通过使用和开发从元形式和解析数论的技术混合解决每个猜想。此外，该补助金还包括一个本科生数论暑期研究项目。 这个暑期课程有不同的目标：增加在数学和科学的代表性不足的少数民族参与;生产一个自定进度的数学调查系列，将提供给一般的在线本科社区;让本科生参与积极的研究调查;并在密苏里州的大学数学系制作新课程。最后，研究人员将进行实验性的努力，以增加研究生的知名度，旅游机会和数学界的专业经验。 美国国家科学基金会强烈鼓励学术教师作为教育工作者和研究人员的早期发展。教师早期职业发展（CAREER）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它在一个单一的计划中结合了最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。该计划增强并强调了基金会对全面，平衡的学术生涯发展的重要性。

9700542 Lieman This award funds programs for research and education centered around the areas of number theory and computational mathematics. In number theory, the investigator will address several outstanding conjectures about the average values of various families of L-series of arithmetic interest, including an "on average" version of the Lindelof hypothesis in n-aspect; a conjecture concerning the Whittaker-Fourier coefficients of metaplectic forms; and a conjecture concerning the average values of the L-series of the classical "sum of two cubes" family of elliptic curves. The investigator expects to resolve each conjecture by using and developing a blend of techniques from metaplectic forms and analytic number theory. In addition, the grant includes a summer research project in number theory for undergraduates. This summer program has diverse goals: to increase underrepresented minority participation in mathematics and science; to produce a self-paced mathematical investigation series which will be available to the general on-line undergraduate community; to involve undergraduates in active research investigations; and to produce new courses for the mathematics department at the University of Missouri. Finally, the investigator will undertake an experimental effort to increase graduate student visibility, travel opportunities, and professional experience within the mathematics community. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation-wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers.