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?
Best Answer
This must have been Heinrich Kornblum (1890-1914).
[note by E. Landau in German, my translation]
$^1$ The author, born in Wohlau on August 23, 1890, had before the war independently made the discovery that Dirichlet's classic proof of the theorem of prime numbers in an arithmetic progression (along with the later elementary reasons for the non-vanishing of the known series) had an analogue in the theory of prime functions in residue classes with a double module ($p,M$). His doctoral dissertation on this self-chosen topic was already essentially finished when, as a war volunteer, he fell in October 1914 at Роёl-Сареllе. Only recently I received from his estate the manuscript (known to me since 1914). I hereby publish the most beautiful and interesting parts. The Kornblum approach is characterized by high elegance and shows that science has lost in him a very promising researcher.