VPW: Generalized P-Adic Local Zeta Functions

这项研究追寻了一些问题，这些问题在一定程度上与私人侦探黛安·迈瑟博士与哈佛大学的卡兹丹教授和马祖尔教授进行的并将继续进行的讨论有关，并受到了这些讨论的启发。Meuser教授正在研究一类广义p-进局部Igusa Zeta函数的性质。一个特例是簇的“p-进体积”，它是紧解析簇X上的解析微分w的积分，她一直在与Kazhdan和Mazur讨论这种情况。她正在详细研究的一个特例是广义Zeta函数，在这种情况下，X是椭圆曲线，w是椭圆曲线上唯一的不变微分。互动活动包括：通过一个女性数学组织与研究生和本科生女性接触，并担任哈佛大学宿舍的教师顾问。

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.