TY - JOUR
TI - The minimal parabolic Eisenstein distribution on the double cover of SL(3) over Q
DO - https://doi.org/doi:10.7282/T32R3VS3
PY - 2017
AB - We begin a study of the Fourier Coefficients of a minimal parabolic Eisenstein distribution on the double cover of SL$(3)$ over $mathbb{Q}$. The central problem in the computation of the Fourier coefficients is a computation of certain exponential sums twisted by the splitting map $s:Gamma_1(4)
ightarrow {pm1}$, which appear after unfolding the integral defining the Fourier coefficients. In cite{M06}, Miller provides a formula for $s$; unfortunately, this formula does not appear conducive to the computation of the exponential sums; however, while considering a similar computation over number fields containing the $4$-th roots of unity, Brubaker-Bump-Friedberg-Hoffstein cite{BBFH07} successfully computed the non-degenerate Fourier coefficients of a minimal parabolic Eisenstein series using a formula for an analog of $s$ in terms of Pl"{u}cker coordinates. These coordinates are well suited to the computation of the exponential sums and so our main objective is a proof that Miller's formula for $s$ can be written in terms of Pl"{u}cker coordinates. With this new formula for $s$ we can compute the Fourier coefficients of our Eisenstein distribution. The calculations of these Fourier coefficients will be addressed in a forthcoming work.
KW - Mathematics
KW - Eisenstein series
KW - Number theory
LA - eng
ER -