I am reading a nice booklet (in Italian) containing the exchange of letters that André and Simone Weil had in 1940, when André was in Rouen prison for having refused to accomplish his military duties.
Of course, among these letters, there is the famous one where André describes his mathematical work to his sister, whose English translation was published in 2005 in the Notices AMS. Referring to this translation, at page 340 we can read
[...] this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants (that is to say, a finite number of elements: also said to be a Galois field, or earlier “Galois imaginaries” because Galois first defined them and studied them; they are the algebraic extensions of a field with p elements formed by the numbers 0, 1, 2,...,p − 1 where one calculates with them modulo p, p = prime number). They appear already in Dedekind. A young student in Göttingen, killed in 1914 or 1915, studied, in his dissertation that appeared in 1919 (work done entirely on his own, says his teacher Landau), zeta functions for certain of these fields, and showed that the ordinary methods of the theory of algebraic numbers applied to them.
My Italian book contains a note at this point, saying
Di questo "giovane studente" non abbiamo altre notizie
that can be translated as
We have no further information about this "young student".
This seems a bit strange to me: if an important result on zeta functions is really due to this student, his name should be known, at least among the experts in the field. So let me ask the following:
Who is the "young student in Göttingen, killed in 1914 or 1915" André Weil is talking about?