Alladi Ramakrishnan Hall

What is NOT known about Eisenstein series ?

S. Boecherer

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The properties of Eisenstein series $\sum_{c,d} (cz+d)^{-k}$
and their higher-dimensional analogues (Siegel modular forms) are well-known as long as we are in the range of absolute convergence.
Furthermore, there is the classical work of Hecke on Eisenstein series
of weight 2, where already some interesting phenomenon appears.
In the higher dimensional case Shimura did some work, but there
remain interesting open problems, which I want to discuss.