Arithmetic theta lifting andL-derivatives for unitary groups, I

Arithmetic theta lifting and L-derivatives for unitary groups, I

Arithmetic theta lifting and L-derivatives for unitary groups, II

Theta Dichotomy for Unitary Groups

Some recent work of Gross and Prasad [14] suggests that the root numbers attached to certain symplectic representations of the Weil-Deligne group of a local field F control certain branching rules for representations of orthogonal groups over F . On a global level, this local phenomenon should have implications for the structure of the value at the center of symmetry for certain L-functions of ...

Theta Correspondence for Unitary Groups

In this paper we study the theta correspondence for Unitary groups of the same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to unify and generalise all these known results in terms of two conjectures, one local and the other global. These conjectures are in terms of the parametrisation of irreducible admissible representat...

Arithmetic Theta Lifts and the Arithmetic Gan–gross–prasad Conjecture for Unitary Groups

In 1980s, Gross–Zagier [GZ86] established a formula that relates the Neron–Tate height of Heegner points on modular curves to the central derivative of certain L-functions associated to modular forms. Around the same time, Waldspurger proved a formula, relating toric periods of modular forms to the central value of certain L-functions. Gross put both of these formula in the framework of represe...