Opera De Cribro

By John B. Friedlander, Henryk Iwaniec. 2010

413 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/28ca3ca827b5dfb11c4ba3c1ed1868ad92ab7a8c

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Multiplicative functions in short intervals (2015, neutral): “Ramar´e’s identity [8, § 17.3]) to extract from the Dirichlet polynomial f ( n ) n ∈S n 1+ it = p 1+ it m 1+ it · # { P ≤ q ≤ Q : q | m } + 1 , where S is the set of integers which have a prime factor from each interval [ P i , Q i ] with i ≤ J except possibly not from [ P j , Q j ].”
Large gaps between consecutive prime numbers (2014, methodology): “the Selberg sieve); we omit the proof here, referring the reader instead(6) to [19] or [11].”
The horocycle flow at prime times (2011, background): “1 can be used together with a lower bound sieve (see [11], Chapter 12) to prove the density of the orbit.”
Expander graphs in pure and applied mathematics (2011, methodology): “y 1. But there are so many summands (approximately 4 p x=logx) which makes the formula quite useless. Various \sieve methods" have been developed for problems like that{the reader is referred to [FI] and [IK], for example. Let us say a few words about the combinatorial sieve developed by Brun. ”
A proof of the positive density conjecture for integer Apollonian circle packings (2010, methodology): “ A (k) =A 0 \[2k;2k +h 2k p k ] where we have (3.4) jA (k)j=h 2k k 1One can in fact extend Lemma 2.3 to show that this holds for every n. Friedlander and Iwaniec do this for a 0 =1 in Theorem 14.4 of [FI]. However, it is not necessary here. A PROOF OF THE POSITIVE DENSITY CONJECTURE FOR INTEGER APOL”
Expansion in finite simple groups of Lie type (2013, background): “[FrIw2010].”