Mathematical Research Letters
Volume 19 (2012)
The derivative of an incoherent Eisenstein series II
Pages: 273 – 289
Let $K$ be an imaginary quadratic field with the norm map$\N$. Let $(K,-\kappa\N)$ be a binary quadratic form with$\kappa$ a positive rational number. In this paper, undersome minor conditions on $\kappa$, we first construct anincoherent Eisenstein series (in the sense of Kudla)associated to $(K,-\kappa\N)$. Then we study its derivativeat the center of symmetry $s=0$, and show that eachnon-constant Fourier coefficient of the derivative can beinterpreted as the degree of certain zero-dimensionalschemes. This result together with our previous work givesa complete answer to a question raised by Kudla–Rapoport–Yang.