POLES OF EISENSTEIN SERIES ON SLN INDUCED FROM MAXIMAL PARABOLICS

The author locates poles for Eisenstein series on algebraic groups SL(n)(DELTA), where n is-an-element-of N and DELTA is an arbitrary finite dimensional division algebra over a number field. An explicit family of nonholomorphic functions, which include series of arbitrary level, is characterized. Each series E(z, s) is induced from a character on a maximal parabolic. For each E(z, s) in the family, there is an explicit product LAMBDA(s) of GAMMA-functions, L-functions and a polynomial term such that LAMBDA(s)E(z, s) has only simple poles in the s variable.