On Stark elements of arbitrary weight and their $p$-adic families
Number Theory
2016-07-25 v1
Abstract
We develop a detailed arithmetic theory related to special values at arbitrary integers of the Artin -series of linear characters. To do so we define canonical generalized Stark elements of arbitrary `rank' and `weight', thereby extending the classical theory of Rubin-Stark elements. We then formulate an extension to arbitrary weight of the refined version of the Rubin-Stark Conjecture that we studied in an earlier article and also show that generalized Stark elements constitute a -adic family by formulating precise conjectural congruence relations between elements of differing weights. We prove both of these conjectures in several important cases.
Keywords
Cite
@article{arxiv.1607.06607,
title = {On Stark elements of arbitrary weight and their $p$-adic families},
author = {David Burns and Masato Kurihara and Takamichi Sano},
journal= {arXiv preprint arXiv:1607.06607},
year = {2016}
}