Thread: Parity barrier
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Old 2020-02-13, 05:52   #4
R.D. Silverman
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Nov 2003

723210 Posts

Originally Posted by R.D. Silverman View Post
With regard to the bilinear forms: The successes have come because the range sets
for these forms have "sufficient density". When one considers (say) X^2 + 1, there
are ~sqrt(B). such integers up to B. But if we take a bilinear form such as x^2 + y^4
there are ~B^(3/4) such integers less than B. This is "just enough more"
so that sieve methods can succeed; the range sets are just a little bit denser.

BTW, I have read Halberstam & Richert's "Sieve Methods" a couple of times. I have
it on good authority from an expert (my ex) that it is a great reference, but not a
great textbook to learn from. I found it frustrating to read and understand. I still
can't claim to understand it, but it is a good starting point.
Does anyone know if Murty's book is a better tutorial?
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