An explicit Waldspurger formula for Hilbert modular forms
  We describe a construction of preimages for the Shimura map on Hilbert modular forms, and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted L-functions. Our construction is inspired by that of Gross and applies to any nontrivial level and arbitrary base field, subject to certain conditions on the Atkin-Lehner eigenvalues and on the weight. 
Nicol\'as Sirolli, Gonzalo Tornar\'ia
math.NT