Explicit formulae of siegel eisenstein series

  title={Explicit formulae of siegel eisenstein series},
  author={Atsushi Haruki},
  journal={manuscripta mathematica},
(0.1) g.~m) :----E det(cz + d) -k (c,a) be Siegel Eisenstein series of degree m, weight k. Here z is a variable of Siegel / \ upper half space H,~ of degree ra, and the sum ( * * ) c(m) d(m runs over a complete \ / /(" :/ ,/\ system of representatives of 0(m) E Sp2m(Z Sp2,~(Z). The right-hand side of (0.1) converges absolutely and locally uniformly if k > m + 1. Siegel [18] proved that the Fourier coefficients of ~k (m) are rational. But for smaller weight cases, another approach is available… CONTINUE READING