The coarse trace formula of GL(4)

Abstract

Trace formula is an important method to study the Langlands program. Arthur obtains the existence of stable trace formula for connected reductive group. In this paper, we will give the explicit coarse trace formula of GL(4). In general case, Arthur applies the truncation operator on the two sides of trace formula, which is convergent. In our case, we will prove that the divergent terms of the two sides of the trace formula of GL(4)$ are equal. We also obtain the explicit formula for ramified orbits of the geometric side of trace formula of GL(4).