Arithmetic of the Asai L-function for Hilbert Modular Forms.
[摘要] Arithmetic of the Asai L-function for Hilbert modular formsAdam Kaye Chair: Kartik PrassannaWe prove two results on rationality of special values of the Asai L-function attached to Hilbert modular forms at critical points. Such L-functions only admit critical values when the Hilbert modular form has non-parallel weight. Our rationality results generalize previous work of Shimura on algebraicity.The first result uses a period defined by transferring the Hilbert modular form to a Shimura curve. The second result uses a period defined using rational structures on the coherent cohomology of Hilbert modular surfaces. We also give some partial results towards integrality of such L-values. Our results are motivated by the study of a p-adic analog of the Beilinson conjecture,which is a deep conjecture relatingalgebraic cycles (and motivic cohomology) to values of L-functions.
[发布日期] [发布机构] University of Michigan
[效力级别] L-functions [学科分类]
[关键词] Number Theory;L-functions;Hilbert modular forms;Special values of L-functions;Beilinson"s Conjecture;Mathematics;Science;Mathematics [时效性]
