WordPress mobile ads

This is rather off-topic, but maybe not all owners of WordPress-hosted blogs are aware of it: since a few days, the mobile version of their sites (which displays when accessed from a phone, or at least from an Android one) displays a small ad-widget by default. I’ve noticed this on Vieux Girondin, Quomodocumque, What’s New, T.Gowers’s blog, etc… Here’s what it looks like:

If this is not the desired behavior (and some of the ads I’ve seen might not be what the owners like to be associated with; the one above is not the worst…) it is probably easy to disable the plugin in charge of the mobile theme (but I can’t check; although my own blog is WordPress-powered, it is hosted at ETH and doesn’t have this plugin).
Also, unfortunately, I don’t know how to check the mobile version from a desktop or laptop computer (presumably one needs to tell the browser to pretend to be a mobile version, but I’ve never learnt how to do that…).

More Kloostermania news

Kloostermania fans can look up what the new version 0.15 does on the Kloostermania page…

In particular, I’ve added the possibility to display Salié sums instead of Kloosterman sums. Precisely, it shows

T(1,-1;p)

instead of T(1,1;p) because the values of the latter are not as interesting, due to the fact that the root s of

X^2=4

modulo a prime are rather simple to compute….

This leads to an intriguing game to play: can you tell the difference between the two types of sums?

First, one must take a prime congruent to 1 modulo 4 (otherwise the Salié sum is zero in that case, which Kloosterman sums never are) for the question to be interesting. Then, there is a kind of theoretical/conjectural answer if you are allowed to look at many instances of the two sums (i.e., you can start the slideshow and observe it for a long time — skipping primes which are 3 mod 4 — without changing the type of sums): their distribution is not the same (conjecturally)! Precisely, the angles θp of the Salié sums, for primes which are 1 modulo 4, defined by

T(1,-1;p)=2\sqrt{p}\cos\theta_p

are equidistributed on [0,π] (for the Lebesgue measure; this is the wonderful theorem of Duke, Friedlander and Iwaniec), whereas one expects those of Kloosterman sums to be distributed according to the Sato-Tate measure

\frac{2}{\pi}\sin^2\theta d\theta.

In particular, the Kloosterman sums should be more often “small”, in some sense, than the Salié sums since the density of the Sato-Tate measure vanishes at θ=0 (which corresponds to a maximal sum).

But what if you’re not allowed to start a long slideshow? For a fixed p, I don’t think one can expect to be able to guess more precisely, just from the values of the sums, than by throwing a coin and choosing Heads/Kloosterman, Tails/Salié. But I wonder if the shapes of the graph of partial sums (as drawn by the program…) could be used to extract more information to lead to a guess with better than even odds of being correct? Or if, at least, it could be used to shorten the length of time one would need to look at the slideshow before being sure of the answer from the distribution perspective?

MSC 2010

For some reason, filling the MSC codes for my papers always feels a bit of a chore; I often have the impression that none of the headings really correspond to what I’ve done, and I’ve found in the past that looking for the right one in a PDF version of the classification is not very efficient. But the tiddlywiki version of the new 2010 classification promises to make things easier: it’s a single HTML file which, through some javascript magic, can be used to dig inside in outliner fashion (expand/unexpand), and which — once downloaded and stored locally — can be freely annotated. Moreover, I can even do that on my android phone and explore the minutiae of the classification during my tramway rides…

But I already noticed that I’ll probably continue feeling perplexed when selecting MSC numbers: for instance, there does not seem to be any item that fits the topic of expander graphs… It seems one has to use an unsatisfactory mixture of 05C40 (“Combinatorics : Graph theory : Connectivity”) and 05C50 (“Combinatorics : Graph Theory : Graphs and linear algebra (matrices, eigenvalues, etc.)”). I’m sure that if I (or anyone else) had pointed this out during the process that ended with the current version of MSC 2010, this would have been corrected, but it is now probably too late until the next revision…

Exponential sums conference

It will probably not come as a surprise to most readers that I like exponential sums, especially over finite fields. I’m therefore very happy to announce a conference on the topic of

Exponential sums over finite fields and applications

that will be held at the Forschungsinstitut für Mathematik of ETH, during the week of November 1 to November 5, 2010. This conference is organized by N. Katz, P. Michel, R. Pink and myself.

The web site

http://www.math.ethz.ch/~kowalski/exponential-sums.html

is now up, with a preliminary list of speakers and an unofficial poster

[Poster]

(the official poster will come soon, its design will link the conference thematically with the other two number theory events that have been organized in Zürich this year, the Number Theory Days and the Rational Points conference.)

As indicated on the web site, there will be some support available for other participants, in particular PhD students and young researchers. Anyone interested in coming is invited to write to the contact email address: expsums@math.ethz.ch