We calculate the period function of Lewis of the automorphic Eisenstein series E(s, w) = 1/2vs ∑n,m≠(0,0)(mw + n) -2s for the modular group PSL(2, ℤ). This function turns out to be the function B(1/2, s + 1/2)ψs(z), where B(x, y) denotes the beta function and ψs a function introduced some time ago by Zagier and given for Rs > 1 by the series ψs(z) = ∑n,m≥1(mz + n)-2s + 1/2ζ(2s) (1 + z -2s). The analytic extension of ψs to negative integers s gives just the odd part of the period functions in the Eichler, Shimura, Manin theory for the holomorphic Eisenstein forms of weight -2s + 2. We find this way an interesting connection between holomorphic and nonholomorphic Eisenstein series on the level of their respective period functions.
|頁（從 - 到）||1-8|
|期刊||Mathematical Physics Electronic Journal|
|出版狀態||Published - 1 12月 1998|