# Talk:Friedlander–Iwaniec theorem

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Field:  Number theory

## References

ref 1. is to a paper which quotes a Bombieri–Friedlander–Iwaniec paper. Neither speaks on the ${\displaystyle x^{2}+y^{4}}$ theorem. Shouldn't it be removed? Kope 06:14, 15 July 2007 (UTC)

I referenced #1 only as a source to demonstrate that the theorem was called the "Bombieri-Friedlander-Iwaniec theorem". Obviously, Friedlander and Iwaniec didn't call it that themselves.
I agree that the article should reference the original paper. But I think it also needs the references I supplied, to establish the name of the theorem. -- Dominus 21:57, 15 July 2007 (UTC)
It's a different theorem. Does not speak about primes of the form ${\displaystyle x^{2}+y^{4}}$. Kope 04:23, 16 July 2007 (UTC)
You're right; thanks for catching this. -- Dominus 14:40, 16 July 2007 (UTC)

This is odd. The reference and the misleading insertion of Bombieri's name as a coauthor of the theorem by Friedlander and Iwaniec should be removed. As it is it is irresponsible and against the mathematical tradition. Why not Friedlander–Iwaniec-Peano theorem (?), since they were using the Peano axioms? Bombieri had nothing to do with the theorem in question, he even didn't dream about anything like this. Bombieri has his Fields medal and there is no need to give him a freebie. -- Wlod (talk) —Preceding undated comment was added at 08:24, 2 January 2009 (UTC).

I made the correction you suggested. Indeed the article was confused about Friedlander-Iwaniec and Bombieri-Friedlander-Iwaniec (which is a result about the equidistribution of primes to large moduli). Moreover Bombieri's asymptotic sieve is not relevant in this context as Bombieri's sieve is effective on almost primes and when the level of distribution is close to 1. Neither of these applies to the Friedlander-Iwaniec theorem. Finally the reference to the some obscure mathematical gazette to establish Bombieri's "priority" has also been removed. I might add some more explanations of the sieve being used later on, and also an explanation of the importance of the theorem. — Preceding unsigned comment added by 173.179.61.172 (talk) 06:02, 25 October 2016 (UTC)

## Sieves

I am glad that the title of the article has been corrected. The article still seems to make a false claims about

• the method used by F-Iw;
• about the sieve theory in general.

I forgot the name of the mathematician, who went back to the original Brun's sieve. I think that F-Iw used his improved Brun's sieve, and developed it further.

I am aware of sieves created or started by Eratosthenes, Brun, Linnik, Selberg, ... but not of any initiated by Bombieri. From what I remember, Bombieri was one of the early pioneers, who continued the work by Linnik and Selberg.

I'll leave the necessary changes to the article to a specialist. -- Wlod (talk) 08:08, 5 January 2009 (UTC)

## Importance

I think that the article should mention why this is important and not just a curios. To wit: the sequence is 'thin' (of natural density 0), and previous results showing the infinitude of primes in sequences have generally been 'thick', and the sieve used in the proof is parity-sensitive (where sieve theory usually has trouble distinguishing numbers with an even and an odd number of prime factors).

Is anyone up to the task?

CRGreathouse (t | c) 15:34, 16 October 2008 (UTC)