VPW: Generalized P-Adic Local Zeta Functions

这项研究的一些问题与私家侦探Diane Meuser博士与哈佛大学Kazhdan教授和Mazur教授的讨论有关，并在一定程度上受到了讨论的启发。Meuser教授正在研究广义p进局部Igusa zeta函数的性质。一种特殊的情况是一种变量的“p进体积”，这种变量是解析微分w在紧化解析变量X上的积分，她已经与Kazhdan和Mazur讨论过这种情况。她正在详细研究的一个特例是广义的ζ函数其中X是一条椭圆曲线w是椭圆曲线上唯一不变的微分。互动活动包括：通过妇女数学组织参与研究生和本科生，并担任哈佛大学宿舍的指导老师。

This research pursues some questions which are related to and inspired in part by discussions the P.I., Dr. Diane Meuser, has had and and continue to have with Professor Kazhdan and Professor Mazur of Harvard University. Professor Meuser is studying properties of a generalized p-adic local Igusa zeta function. A special case is the "p-adic volume" of a variety which is the integral of the analytic differential w on a compact analytic variety X and it is this case that she has been discussing with Kazhdan and Mazur. A special case she is working on in detail is the generalized zeta function in the case where X is an elliptic curve and w is the unique invariant differential on the elliptic curve. Interactive activities include: involvement with graduate and undergraduate women through a Women in Mathematics organization, and serving as a faculty advisor to a residence hall at Harvard University.