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arXiv · 1607.06607

On Stark elements of arbitrary weight and their $p$-adic families

David Burns·Masato Kurihara·Takamichi Sano
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Abstract

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.

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David Burns, Masato Kurihara, Takamichi Sano. 2016-07-22. On Stark elements of arbitrary weight and their $p$-adic families. https://arxiv.org/abs/1607.06607

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