I spent some time today looking for any biographical information on Jitsuro Nagura and came up empty-handed. Any suggestions welcome.

Also, the Wiki note on the Chebyshev $\psi$ function says that von Mangoldt proved in 1895 that

$\psi_0(x) = x - \sum_{\rho}\frac{x^{\rho}}{\rho}- \frac{\xi'(0)}{\xi(0)}-\frac{1}{2}\ln(1-x^2) $

There is a reference to a 1903 note by E. Schmidt which may or may not contain a reference to the original paper, but my amateurish search (in Euclid, JSTOR) did not turn up anything.

Thanks in advance.

Edit: have changed the title to reflect that I am seeking information on J. Nagura and have found the other reference. Thanks.

  • $\begingroup$ It looks like a Japanese name, and it's published in a Japanese journal, so if I may hazard a guess, I'd say he's Japanese... Unfortunately the communicating editor (Zyoiti Suetuna, 末綱恕一) is deceased, so that's one avenue of pursuit gone... $\endgroup$ – Zhen Lin Jan 10 '12 at 10:57
  • $\begingroup$ Yes, I saw that the journal was Japanese, and the article is in subtly unidiomatic English, so I surmise the author was native Japanese--possibly at the peak of his powers during a somewhat distracting moment in Japanese history. $\endgroup$ – daniel Jan 10 '12 at 11:10
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    $\begingroup$ Hum, my best guess from the romaji is that Jitsuro Nagura could be written 名倉実郎. One may try writing a letter to The Japan Academy to see if they can dig something up. @Zhen: even without the communicating editor, one can hope that some scrap of paper would've survived with his listed address / institute. $\endgroup$ – Willie Wong Jan 10 '12 at 15:16
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    $\begingroup$ @Willie: Actually, given that simplified kanji (新字体) were only promulgated in 1946, the spelling of his name most likely does not contain the character 実... $\endgroup$ – Zhen Lin Jan 11 '12 at 17:25
  • $\begingroup$ @Zhen: ah. Good point. The equivalent character most likely would be 實 in 旧字体. That difference is likely negligible compared to my poorly-informed reconstruction of the likely characters. $\endgroup$ – Willie Wong Jan 12 '12 at 13:32

You can found the paper of von Mangoldt here (it's in German though). I searched for the reference in http://scholar.google.com/ and then looked for the reference on ordinary Google. Other good places to look for old mathematical references are the Zentralblatt and MathSciNet (more recent though).

  • $\begingroup$ This is great and I will note your search path for future reference. $\endgroup$ – daniel Jan 9 '12 at 21:25

This is a partial answer to my question about Jitsuro Nagura, if anyone else happens to be interested. His Japanese name, in Chinese characters, is 奈倉実郎, which is similar except for the first character to that suggested by Willie above.

The Japan Academy reports that they have only two pieces of information about JN. First, he was born prior to 1918 and has a son, Riishi, who was born in 1938. Second, that son was a professor of electrical engineering at Himeji Institute of Technology and Kanagawa Institute of Technology. He was also an employee of the Japan Electronics Company, NEC. An anonymous correspondent at Kanagawa shared: "I am regret to say but Professor Nagura is no longer work for us." This has the ring of truth and JN's son is no doubt retired.

The paucity of information is amazing to me, and I intend to pursue it further, time allowing. Meanwhile, if anyone comes across anything more, I would be very interested.

Update (2/12): Nagura was an "early graduate" of Tokyo University (math major). Since Nagura's paper on primes was published in 1952, it is difficult to know whether he attended Tokyo University under its present name or the pre-1947 designation, Tokyo Imperial University.

Update (6/13): A paper with basic biographical information and a photo of Nagura as a young man in BSHM.

Update (8/13): Teiji Takagi, whose doctoral advisor was David Hilbert, was actively involved in cryptography during WW2. According to Nagura's son, Takagi was a professor of Nagura's at Tokyo Imperial university (possibly his advisor). It seems quite possible that Nagura also helped in the cryptography effort but it would be hard to verify.



MIchael already provided a GDZ link (many old german papers are available there). A french translation of von Mangoldt's work is available at Numdam : 'Sur le Mémoire de Riemann relatif au nombre des nombres premiers inférieurs à une grandeur donnée'. Edwards excellent book concerning zeta should be helpful too!

Concerning Nagura I found nothing except his famous paper sorry...


There is now available a biographic paper of him:

Daniel Tisdale (2013) Sieve of war: the legacy of Jitsuro Nagura, BSHM Bulletin: Journal of the British Society for the History of Mathematics, 28:3, 143-155, DOI: 10.1080/17498430.2013.793949


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