Skip to main content
keoxkeox's user avatar
keoxkeox's user avatar
keoxkeox's user avatar
keoxkeox
  • Member for 7 years, 6 months
  • Last seen more than 5 years ago
About

Mathematicians have always been fascinated by the problem of describing all solutions in whole numbers x,y,z to algebraic equations like

x2 + y2 = z2

Euclid gave the complete solution for that equation, but for more complicated equations this becomes extremely difficult. Indeed, in 1970 Yu. V. Matiyasevich showed that Hilbert's tenth problem is unsolvable, i.e., there is no general method for determining when such equations have a solution in whole numbers. But in special cases one can hope to say something. When the solutions are the points of an abelian variety, the Birch and Swinnerton-Dyer conjecture asserts that the size of the group of rational points is related to the behavior of an associated zeta function ζ(s) near the point s=1. In particular this amazing conjecture asserts that if ζ(1) is equal to 0, then there are an infinite number of rational points (solutions), and conversely, if ζ(1) is not equal to 0, then there is only a finite number of such points.

Badges
This user doesn’t have any gold badges yet.
This user doesn’t have any silver badges yet.
8
bronze badges
Top tags
1
Score
2
Posts
100
Posts %
1
Score
2
Posts
100
Posts %
Top posts
question
2
Nov 8, 2016
answer
1
Jul 19, 2017