Hirzebruch-Zagier classes and rational elliptic curves over quintic fields

Abstract: In joint work with Zhaorong Jin, we establish new instances of the BSD-conjecture for rational elliptic curves over quintic fields. The proof is p-adic in nature and relies on the comparison of two rigid analytic functions: the automorphic p-adic L-function retaining information about special L-values, and the motivic p-adic L-function arising from cycles on Shimura threefolds. The construction of the latter function is of independent interest as it could be applied to other settings related to the Gan-Gross-Prasad conjecture.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar