Title: IDENTITIES ARISING FROM GAUSS SUMS FOR SYMPLECTIC AND ORTHOGONAL GROUPS
Abstract: We express Gauss sums for symplectic and orthogonal groups over finite fields as averages of exponential sums over certain maximal tori.Together with our previous results, we obtain some interesting identities involving various classical Gauss and Kloosterman sums.w F (t) = wF (t)w -1 .In this paper, we apply the above formula to calculate the Gauss sums for Sp 2n , GSp 2n , SO ± 2n , and SO 2n+1 (Theorems 3.1, 3.2, 3.5, 3.6, and 3.7).Combined with the second author's previous results cited above, these yield new