Đề tài " Elliptic units for real quadratic fields "

Elliptic units, which are obtained by evaluating modular units at quadratic imaginary arguments of the Poincar´e upper half-plane, provide us with a rich source of arithmetic questions and insights. They allow the analytic construction of abelian extensions of imaginary quadratic fields, encode special values of zeta functions through the Kronecker limit formula, and are a prototype for Stark’s conjectural construction of units in abelian extensions of number fields. Elliptic units have also played a key role in the study of elliptic curves with complex multiplication through the work of Coates and Wiles....