Fourier coefficients of Siegel-Eisenstein series of odd genus
Generalizing a well-known result (in the case of genus 2) of Eichler and Zagier, the second named author proved an explicit formula for the Fourier coefficients of the holomorphic Siegel-Eisenstein series on the full Siegel modular group of even genus [see Math. Ann. 322, No. 4, 787--809 (2002; Zbl 1004.11020)]. In the paper under review it is shown that a suitable modification of the previous arguments leads to an explicit formula in the case of odd genus as well. In the odd case, only modified divisor sums (and no generalized class numbers as in the even case) enter the final result. Together with the results of the previous work quoted above, the results of this paper give new explicit expressions for all the Fourier coefficients of Siegel-Eisenstein series of both even and odd genus.
scientific article; zbMATH DE number 5810262