# Who is the "young student" André Weil is referring to in his letter from the prison?

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

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:

Question. Who is the "young student in Göttingen, killed in 1914 or 1915" André Weil is talking about?

• A bit of nitpicking: actually André Weil was in prison in Rouen, not in Le Havre.
– abx
Commented Nov 4, 2020 at 15:21
• @abx: thank you for the comment. My booklet says "Le Havre" and, in fact, I did not check before asking here. In Wikipedia page en.wikipedia.org/wiki/Andr%C3%A9_Weil we can read "Weil returned to France via Sweden and the United Kingdom, and was detained at Le Havre in January 1940. He was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen." It is not clear from this when he was transferred from Le Havre to Rouen. The 14-pages letter to Simone is dated March 26, 1940. Commented Nov 4, 2020 at 15:39
• Yes, in fact the letter (in his collected works) starts with "Rouen, 26 mars 1940".
– abx
Commented Nov 4, 2020 at 15:45
• You are right. I corrected the post, thanks again. Commented Nov 4, 2020 at 15:47
• hsm.stackexchange.com/questions/11771/who-was-heinrich-kornblum Commented Nov 5, 2020 at 12:53

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.

• Does the dagger indicate being dead or is it a footnote? Commented Nov 5, 2020 at 11:15
• @msh210 Deceased. There are no footnotes in the indexed by a dagger.
– Jam
Commented Nov 5, 2020 at 15:06
• "The dagger usually indicates a footnote if an asterisk has already been used." ... but, in this case: "The dagger is also used to indicate death ... When placed immediately before or after a person's name, the dagger indicates that the person is deceased." [ source ] Commented Nov 5, 2020 at 17:39
• @msh210 A "Nachlass" is written after the person cited is deceased, so the "dagger" means "died". (If it indicated a footnote, it would be written in "superscript" style) Commented Nov 6, 2020 at 10:06
• @David Tonhofer: Actually, here Nachlass (legacy) refers to papers the deceased person wrote during his lifetime and were found after his death. It is not that somebody else writes the Nachlass, but it may be edited, of course. Commented Nov 11, 2020 at 13:56

That was most certainly Heinrich Kornblum. His paper titled 'Über die Primfunktionen in einer arithmetischen Progression' was published in Math. Z. 5 (1919) pp 100–111 (EuDML), see the zbMath revew. In the paper he establishes the analogue of Dirichlet's theorem on primes in arithmetic progressions, in the polynomial setting (with natural density).

His history and contribution are mentioned several times in Roquette's historical account of the Riemann Hypothesis in positive characteristic.

• Thank you for the answer. Having to choose between two excellent contributions, I accepted Carlo's one because he answered first. Commented Nov 5, 2020 at 6:47