Siegel zeros of Eisenstein series

Research paper by Joseph Hundley

Indexed on: 04 Dec '05Published on: 04 Dec '05Published in: Mathematics - Number Theory


If E(z,s) is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z,s) has a "Siegel zero." That is E(z,\beta)=0 for a real number \beta just to the left of one. We give a generalization of this result to Eisenstein series formed with real valued automorphic forms on a finite central covering of the adele points of a connected reductive algebraic group over a global field.