Archive for August, 2016

Who was Joseph Ser ?

August 25, 2016

In an interesting paper, Iaroslav Blagouchine has presented, among other things, the equivalence of the explicit analytic continuation of \zeta due to Hasse  (in this 1930 paper) \zeta(s)=\frac{1}{1-s}\sum_{n=0}^{\infty}\frac{1}{n+1}\sum_{k=0}^n(-1)^k \begin{pmatrix}n\\ k\end{pmatrix} (k+1)^{1-s}  with one derived 4 years earlier by a Joseph Ser (in this paper) \zeta(s)=\frac{1}{1-s}\sum_{n=0}^{\infty}\frac{1}{n+2}\sum_{k=0}^n(-1)^k \begin{pmatrix}n\\ k\end{pmatrix} (k+1)^{-s}.

It may be that these could help improve the situation regarding the location of the non-trivial zeros of \zeta, although of course the classical Mertens approach with logs and the trigonometric identity cannot be mimicked here due to the ever growing number of terms added for each new n.

But who was Joseph Ser then ? There’s a short wikipedia bio saying that nothing much is known about him. There seems to be a genealogical entry for him here, with little more details beyond dates.  I couldn’t find his name among Normaliens nor Polytechniciens. He also doesn’t appear in the list of pre-1901 professeurs agrégés, and neither in the list of PhDs compiled by Hélène Gispert in her book.

As for published material, Numdam has 3 papers from him, where only the earliest one has a tiny indication: Nantes.  One can also find that a book of Ser, Les Calculs Formels des Séries de Factorielles, got a quite unfavorable review  in Bull AMS, while the same book got a more positive review in L’Enseignement Mathématique. And finally, he seems to have authored several articles in Mathesis, at least until 1953 when he was well into his seventies.

Feel free to comment if you know more about his work and career.

20160824_170956Caniculaire. (Metz, late august 2016, Public Domain.)

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Further august 2016 news

August 18, 2016

[Posted on august 18, 2016.]

In no particular order :

  • there is a website to gather comments on the forthcoming MSC 2020 (one obvious set of candidates not yet mentionned are the various perfectoid structures–Peter Scholze had used a bunch of MSC 2010 classes, but with more than 120 citations to that paper by now it is clear new ones are needed)
  • statistics papers in Inventiones are very rare, so this one must be outstanding
  • Cédric Villani will give a public lecture in Mumbai tomorrow
  • a student who ranked joint first at this year’s highly difficult competitive exam to enter l’X credits the book What is mathematics (2nd edition) by Courant, Robbins and Stewart, which he read while in eleventh grade (première), for giving him a passion for maths
  • also joint first was Cécile Gachet, who equally ranked first at the even more difficult competitive exam to enter ÉNS Ulm (this feat was obviously saluted, e.g. on twitter)
  • the MSRI program on Geometric Group Theory has just started, with in particular an introductory workshop next week
  • there’s an interesting article on special values of Zeta functions in the september issue of Notices of the AMS (including \zeta(2) as the volume of a moduli space)
  • topically, this blog’s host has attempted to come up with something at least remotely interesting a few weeks ago, it didn’t go so well as usual, but hopefully the first section is indeed new and worthy of publication, we shall see…

20160813_072506Louis XVIth, the seagull, and the antiparallelogram at dawn.

Nantes, august 2016 (public domain).

Some august 2016 news: Epiga, mathinfoly, …

August 8, 2016

[Posted on august 8, 2016.]

  • The first mathematics journal produced by Episciences.org, a platform for arXiv overlay journals, has been listed recently. It is Epiga, which stands for Épijournal de Géométrie Algébrique.  (Well, technically there is also the Hardy-Ramanujan journal, which previously existed as a paper journal and which adopted the Episciences platform in 2014, but it hasn’t published anything  for a year and a half.)    The editorial board of Epiga looks like it contains many very distinghuised people, so while it has not published any papers yet, it will probably be a high-quality journal. Let’s see how that pans out…
  • Jumping to another topic, it is fantastic that a summer school for interested high-schoolers, mathinfoly2016, will take place in a fortnight at ENS Lyon : the set of speakers looks great and diverse (and it includes in particular recent EMS prize winner Vincent Calvez). The courses will be completely in french (which is better for that age group I think).
  • At CIRM the semester on Ergodic Theory and Dynamical Systems and their Applications to Number Theory (within the setting of a Jean Molet Chair to Mariusz Lemańczyk) has just started.    One can still register to the december conference (which has an impressive list of speakers and a scientific comitee that includes Artur Avila–is he turning his powers to Number Theory? That would be great!) as well as to the doctoral school (deadline early september).
  • Finally there’s a nice portrait here of Jean-Pierre Serre, who turns 90 this year, on the occasion of a talk he gave last month in Bordeaux. He still has “projects in the fridge”!

Pic du Cap Roux, Antheor Saint-Raphael, by Cedric Biennais on flickr