Article: Prime Numbers Get Hitched

[ComputerGeek]

Anyone read this?

What do you think?

http://www.seedmagazine.com/news/2006/03/prime_numbers_get_hitched.php?utm_source=seedmag-main=rss

 

[mathwonk]

i can only read the first page, which gets nowhere.

 

[ComputerGeek]

why can you only read the first page? There should be a "next" link at the bottom.

 

[mathwonk]

well he is obviously a real mathematician, and a very gifted writer for the public as well. he is one of those articulate and intelligent people, frequently british, who make math seem fun and exciting and appealing to the general public.

it is a good thing for math that he is around.

 

[mathwonk]

there is no next link at the bottom, only a previous link that does not work.

 

[mathwonk]

I used a different browser and was able to read it. it was delightful, but gives no mathematics of course so one cannot judge any of his statements. still he is a reliably published number theorist with a paper in the Annals of Math, and a professor at oxford i believe, hence highly trustworthy.

 

[shmoe]

It is all pretty well known stuff in number theory circles.

The 42 they mention is just a conjecture at this point, the asymptotic for the 6th moment has yet to be proven (I much prefer calling it "6th" moment over "3rd", it has a power of 6 of zeta). Conrey and Gonek had a conjeture for the corresponding number in the 8th moment by other means. As the story goes, Keating was about to give a lecture announcing their general conjecture when Conrey informed him of his own version for the fourth. In much excitement they worked out what Keating and Snaith's general version gave on a blackboard just before the talk. Sure enough it was a match at 24024, adding even more weight to their general conjecture.

I can't say I understand all of Keating and Snaiths work, but the general idea is simple enough. If the zeros of the zeta function can be modeled by large random unitary matrices, then the values of zeta could be modeled by the characteristic polynomials of said matrices. Neat stuff.

One of the purposes to studying these moments is to get a handle on the values of zeta on the critical line. One of the goals would be to prove the long standing Lindlehof hypothesis, which is a straight up bound on the critical line. It's weaker than the riemann hypothesis, but still gives some info on the zeros.