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Character expansion developed in real space renormalization group (RSRG)approach is applied to U(1) lattice gauge theory with $\th$-term in 2dimensions. Topological charge distribution $P(Q)$ is shown to be of Gaussianform at any $\b$(inverse coupling constant). The partition function $Z(\th)$ atlarge volume is shown to be given by the elliptic theta function. It providesthe information of the zeros of partition function as an analytic function of$\ze= e^{i \th}$ ($\th$ = theta parameter). These partition function zeros leadto the phase transition at $\th=\pi$. Analytical results will be compared withthe MC simulation results. In MC simulation, we adopt (i)``set method" and(ii)``trial function method".Comment: 14 pages, plaintex, 4 figure

Character Expansion, Zeroes of Partition Function and -Term in U(1) Gauge Theory