A Virtual Proof

In this chapter I would like to interrupt the historic line in order to put into evidence what I just said, namely that the proof of RHp could have been found already in 1937, in the framework of the theory of function fields. I will present here such a proof. In principle it can be regarded as a translation of Severi’s proof from the language of algebraic geometry into the language of algebra. But I will not use any knowledge of the terminology and results of algebraic geometry. I shall use those notions and facts from the theory of function fields which were available to and preferred by Hasse at the time of the Gottingen workshop which I have discussed above.