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The negative Pell equation and Stevenhagen's conjecture

Posted in
Speaker: 
Peter Koymans
Affiliation: 
MPIM
Date: 
Wed, 2021-07-07 14:30 - 15:30
Parent event: 
Extra talk

(50 min. lecture + 10 min. discussions)

Lecture by Peter Koymans:
Meeting ID: 912 3490 0709 Passcode: 671511
https://zoom.us/j/91234900709?pwd=bUFhQjRGQ3BJc1ppdSttWWF4VGkxZz09

Pell's equation, $x^2 - Dy^2 = 1$, has been studied since at least the ancient Greeks. It is well-known that Pell's equation is non-trivially soluble
in integers $x$ and $y$ for every squarefree integer $D > 1$. However, the negative Pell equation $x^2 - Dy^2 = -1$ is much more mysterious.
In 1995 Peter Stevenhagen conjectured an asymptotic formula for the number of squarefree integers $D \le X$ for which the negative Pell
equation is soluble. In this talk I will discuss Stevenhagen's conjecture and its recent resolution by Carlo Pagano and myself.

 
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