Evaluation of L-series and Explorations in Mathematics

9700542莱曼该奖项为围绕数论和计算数学领域的研究和教育项目提供资金。在数论中，研究者将解决关于L算术兴趣级数各族的平均值的几个未决猜想，包括n方面的“平均”版本的林德洛夫假设；关于亚辛形式的惠特克-傅立叶系数的猜想；以及关于经典的“两个立方之和”椭圆曲线族的L级数的平均值的猜想。研究人员期望通过使用和发展亚可解形式和解析数论的混合技术来解决每一个猜想。此外，助学金还包括一项面向本科生的数论暑期研究项目。这个暑期项目有不同的目标：增加少数族裔在数学和科学方面的参与；制作一个自我调整进度的数学调查系列，供普通在线本科生社区使用；让本科生参与积极的研究调查；并为密苏里大学的数学系制作新的课程。最后，研究人员将进行一项实验，以增加研究生在数学界的能见度、旅行机会和专业经验。国家科学基金会强烈鼓励学术人员的早期发展，既是教育工作者，也是研究者。学院早期职业发展(Career)计划是一个基础范围的计划，为初级教师在其整体职业发展的背景下提供支持。它在一个单一的计划中结合了对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。这一计划加强并强调了基金会对充分、平衡的学术事业发展的重要性。

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.