Analytic Continuation of the Unknown Functions in the Genus 1 Case

In Sect. 2.5, we have shown, using the Riemann surface S, that the functions pi and (pi) over tilde could be analytically continued to D1+epsilon. In this chapter, we shall propose other methods of analytic continuation, which in a sense are more effective, since they allow in fact a continuation to the whole complex plane. We consider only parameter values ensuring the Riemann surface S to be of genus 1, according to the study made in Sect. 2.3.