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At first a type of Eisenstein series is defined as distributions givingnearly-holomorphic automorphic forms on a totally real field, with differentexpressions (integral, summation) ; then these are shown to satisfied theexpected properties, and the Fourier coefficients are explicitly computed.Finally, an explicit computation shows that in the simplest case, the abstractobject considered simplify down to the most classical version of Eisensteinseries.

Distributions de s\'eries d'Eisenstein presque holomorphes sur un corps totalement r\'eel