Résume | In the theory of modular forms, Eisenstein series plays animportant role because of its explicit Fourier coefficients. It iswell-known that the algebra of modular forms on $SL_2(\mathbb{Z})$ isgenerated by the classical Eisenstein series $E_4$ and $E_6$. For a fixedweight $k$, Kohnen and Zagier showed that it suffices to consider the spanof the products of two Eisenstein series $E_\ell$ and $E_{k - \ell}$. Inthis talk, we will look at a related question, first raised by TonghaiYang, about the span of the restrictions of coherent Eisenstein series. Wewill discuss the construction of these Eisenstein series, its relationshipto special values of L-function, and other related open problems. |