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Category Archives: Mathematics

Trace functions, a survey

At last count, my series of works with Étienne Fouvry and Philippe Michel on trace functions and their applications consists of seven research papers or preprints, amounting to a bit more than 200 pages. To these are added a number of works-in-progress or partial notes (some with results we did not need or use and [...]

James Maynard, auteur du théorème de l’année

How many times in a year is an analytic number theorist supposed to faint from admiration? We’ve learnt of the full three prime Vinogradov Theorem by Helfgott, then of Zhang’s proof of the bounded gap property for primes. Now, from Oberwolfach, comes the equally (or even more) amazing news that James Maynard has announced a [...]

Our research institute has a nicer logo than yours

Here is the logo of the new Institute for Theoretical Studies of ETH:

Conductors of one-variable transforms of trace functions

In one of the recent posts by T. Tao on the progress of the Polymath8 project, the question arose of whether such functions as defined for and a rational function , are trace functions, and more importantly, what is their conductor (see this, and the following, comments). In particular, if is obtained by reduction modulo [...]

Sliding over the Polya-Vinogradov gap

In my series of papers with É. Fouvry and Ph. Michel, we seem to alternate between longer papers and shorter ones. The last one, which we just put up on arXiv, is in some sense the shortest one: even if it goes up to 19 pages in length, the basic idea can be explained extremely [...]