Selberg Zeta Functions over Function Fields Original Research Article

We compute explicitly the Selberg trace formula for principal congruence subgroups of PGL(2, imageq[t]) which is the modular group in positive characteristic cases. We also express the Selberg zeta function as a determinant of the Laplacian which is composed of both discrete and continuous spectra. All factors are calculated explicitly, and they are rational functions in q−s.