Early january 2017 items

[Posted on january 4, 2017.]

Two very recent things:

  • Danylo Radchenko and Maryna Viazovska have released an interesting preprint on Fourier interpolation on the real line, and while I do not understand it in any depth I’ve noticed that a formula at the end of section 7, namely that for odd Schwartz functions f one has f'(0)+\sum_{n=1}^{\infty}\frac{r_3(n)f(\sqrt{n})}{\sqrt{n}}=i\widehat{f'}(0)+ \sum_{n=1}^{\infty}\frac{r_3(n)i\widehat{f}(\sqrt{n})}{\sqrt{n}} (where r_3(n) is the number of representations of n as a sum of 3 squares) is exactly the little-known formula of Guinand that Yves Meyer rediscovered at the end of 2015 (see equation 9 in his now freely available PNAS paper) and which has already been mentionned on this blog and on MO (so I’ve told Radchenko and Viazovska about Meyer’s paper). That’s nice to see such a beautiful formula rediscovered twice and by different means! There must be deep and interesting connections between those two areas of math then…
  • at the Bourbaki seminar next week Harald Helfgott will lecture on the much heralded work of László Babai on the Graph Isomorphism Problem, and Helfgott has just announced that he could check most of the proof but had found an error in the time analysis, partly corrected by Babai, who has just issued a notice about the issue.

Stern Clara und Hilli by Kerstin (aka Ella T.) on flickr

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: