Arithmetic of the Asai L-function for Hilbert Modular Forms.

Number Theory;L-functions;Hilbert modular forms;Special values of L-functions;Beilinson"s Conjecture;Mathematics;Science;Mathematics

Kaye, Adam RubinDebacker, Stephen M ;

University of Michigan

关键词: Number Theory;    L-functions;    Hilbert modular forms;    Special values of L-functions;    Beilinson";    s Conjecture;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/120693/adamkaye_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.