2016/07/22 by Burns, David, Kurihara, Masato, Sano, Takamichi
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1607.06607
We develop a detailed arithmetic theory related to special values at arbitrary integers of the Artin L-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 p-adic family by formulating precise conjectural congruence relations between elements of differing weights. We prove both of these conjectures in several important cases.