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

Abstract

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