Arithmetic of the Asai L-function for Hilbert modular forms
Adam Kaye
Chair: Kartik Prassanna
We 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 relating
algebraic cycles (and motivic cohomology) to values
of L-functions.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120693/1/adamkaye_1.pd
