A few things

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Why I finally won't go for open-source analytics tool (for now)

You discovered Google Analytics a few years ago (a webmaster tool to see how many visits on your websites), and used it efficiently. But, you know, Google-centralized internet, etc. and then you thought "Let's go self-hosted and open-source!". And then you tried Piwik and Open Web Analytics.

I did the same. After a few months, here are my conclusions.

Open Web Analytics has a great look, close to Google Analytics, but every week, I had to deal with new issues:

Nearly 250 MB analytics data in 2 weeks (for only a few small websites), this means more than 6 GB of analytics data per year in the MySQL database! ... or even 60 GB per year if you have 100k+ pageviews. That's far too much for my server. This was (nearly) solved by disabling Domstream feature. (Ok Domstream is a great feature, but I would have liked to know in advance that this would eat so much in the database).

I'm not saying OWA is bad: Open Web Analytics is a good open-source solution, but if and only if you have time to spend, on a regular basis, on configuration issues, which I sadly don't have.

I tried Piwik very quickly. It really is a great project but:

So, conclusion:

Analytics, unsolved problem.

I'm still looking for a lightweight self-hosted solution. Until then, I'll probably have to use Google Analytics again.

PS: No offence meant: most of my work is open-source too, and I know that it takes time to build a stable mature tool. This post is just reflecting the end-of-2016 situation.

Somme d'exponentielles concernant la fonction de Möbius

Au cours de mon Master 2, en 2007, j'ai eu l'occasion de considérer une somme d'exponentielles concernant la fonction de Möbius:

$$S(x, \theta) = \sum_{n \leq x} \mu(n) e^{2 i \pi n \theta}.$$

En suivant Maier et Sankaranarayanan, il s'agissait de comparer plusieurs preuves du résultat suivant.

Théorème. Soit $\theta$ un nombre irrationnel de type $1$. Alors pour tout $\varepsilon > 0$, on a $$S(x,\theta) \ll x^{4/5 + \varepsilon},$$

où le type d'un irrationnel $\theta$ est défini par

$$\eta = \sup \{\delta > 0 : \liminf_{q \rightarrow \infty} q^\delta \| q \theta \| = 0 \}.$$

et $\| x \|$ est la distance d'un réel $x$ au plus proche entier.

Le mémoire Sur une somme d'exponentielles concernant la fonction de Möbius contient la démonstration de ce théorème ainsi qu'un contenu (très) introductif aux caractères de Dirichlet, fonctions $L$.

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