Article: Prime Numbers Get Hitched

In summary, the article discusses the conjecture that there is a fourth moment of zeta, and how it was matched by Keating and Snaith. It also discusses the importance of moments in mathematics.
Physics news on Phys.org
  • #2
i can only read the first page, which gets nowhere.
 
  • #3
why can you only read the first page? There should be a "next" link at the bottom.
 
  • #4
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.
 
  • #5
there is no next link at the bottom, only a previous link that does not work.
 
  • #6
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.
 
Last edited:
  • #7
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.
 

1. What are prime numbers?

Prime numbers are numbers that are only divisible by 1 and itself. They are greater than 1 and cannot be written as a product of other numbers.

2. Why are prime numbers important?

Prime numbers have many important applications in mathematics, computer science, and cryptography. They are the building blocks of all other numbers and are also used in algorithms for data encryption and security.

3. How are prime numbers determined?

Prime numbers are determined by checking all numbers less than the given number and seeing if any of them can divide evenly into it. If not, the number is prime. This process is called prime factorization.

4. What is the significance of the newly discovered prime numbers?

The discovery of new prime numbers is significant because it expands our understanding of the patterns and properties of prime numbers. It also has potential applications in cryptography and number theory.

5. Can any number be a prime number?

No, not all numbers can be prime numbers. Any number that is divisible by more than two numbers (1 and itself) is not a prime number. In other words, any number that has factors other than 1 and itself is not a prime number.

Similar threads

Replies
8
Views
261
  • Programming and Computer Science
Replies
14
Views
1K
  • Linear and Abstract Algebra
Replies
2
Views
990
Replies
1
Views
741
Replies
7
Views
1K
  • Linear and Abstract Algebra
Replies
4
Views
2K
Replies
8
Views
1K
  • Linear and Abstract Algebra
Replies
11
Views
2K
  • Linear and Abstract Algebra
Replies
6
Views
6K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
Back
Top