Thread: Parity barrier
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Old 2020-02-13, 04:47   #1
CRGreathouse
 
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Aug 2006

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Default Parity barrier

Silverman suggested talking about some real mathematics, maybe the parity problem. I don't know if we have enough expertise here for a good discussion, but I thought I'd give it a go.

Tao has some great expository articles:
https://terrytao.wordpress.com/2007/...-sieve-theory/
https://terrytao.wordpress.com/2014/...m-obstruction/
https://terrytao.wordpress.com/2015/...-sieve-theory/
https://terrytao.wordpress.com/2014/...bounded-error/
https://terrytao.wordpress.com/2016/...mptotic-sieve/

Here are some papers showing real results breaking the parity barrier: Friedlander & Iwaniec, Heath-Brown, Helfgott, Heath-Brown & Moroz, Ramaré & Walker, Tao, and Zhang.

It's hard,and there are still no general techniques, but it's doable. Bilinear forms seem to be a recurring theme.
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