In number theory, the Selberg sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which...

turned to sieve theory, a previously neglected topic which Selberg's work brought into prominence. In a 1947 paper he introduced the Selberg sieve, a method...

small sieves such as the Selberg sieve wherein only a few residue classes are removed. The method has been further heightened by the larger sieve which...

Goldston-Pintz-Yıldırım sieve (also called GPY sieve or GPY method) is a sieve method and variant of the Selberg sieve with generalized, multidimensional sieve weights...

Modern sieves include the Brun sieve, the Selberg sieve, the Turán sieve, the large sieve, the larger sieve and the Goldston-Pintz-Yıldırım sieve. One of...

sieve. Halberstam & Richert remark:: 221  "Thus it is not true to say, as has been asserted from time to time in the literature, that Selberg's sieve...

such as the Brun sieve and Selberg sieve. However, since these more powerful sieves are extensions of the basic ideas of the Legendre sieve, it is useful...

larger sieve is a sieve invented by Patrick X. Gallagher. The name denotes a heightening of the large sieve. Combinatorial sieves like the Selberg sieve are...

449), (457,463), (461,467). D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical...

theorem Brun sieve Function field sieve General number field sieve Large sieve Larger sieve Quadratic sieve Selberg sieve Sieve of Atkin Sieve of Eratosthenes...

MR 3272929. S2CID 55175056. Polymath, D.H.J. (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical...

and named by Atle Selberg in 1949. Beginning around 1996, John Friedlander and Henryk Iwaniec developed some parity-sensitive sieves that make the parity...

Jurkat–Richert theorem, joint work with Wolfgang B. Jurkat that improved the Selberg sieve and is used in the proof of Chen's theorem.: 257  Richert also produced...

Volume 179 (2014), Issue 3 D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical...

From the Polymath8 project. Polymath, D.H.J. (2014), "Variants of the Selberg sieve, and bounded intervals containing many primes", Research in the Mathematical...

Retrieved 2023-12-13. Ben Green and Terence Tao, Restriction theory of the Selberg sieve, with applications, Journal de Théorie des Nombres de Bordeaux 18 (2006)...

MR 3272929. S2CID 55175056. D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical...

structure in the error term in the Selberg sieve, discovered by himself. Later this idea of exploiting structures in sieving errors developed into a major...

2014.8.2067. MR 3294387. Polymath, D.H.J. (2014). "Variants of the Selberg sieve". Research in the Mathematical Sciences. 1 (12). arXiv:1407.4897. doi:10...

MR 3272929. S2CID 55175056. D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical...

the sieve of Eratosthenes", A. Y. Cheer and D. A. Goldston, Mathematics of Computation 55 (1990), pp. 129–141. "An improvement of Selberg’s sieve method"...

2009-03-14. Jurkat, W. B.; Richert, H.-E. (1965). "An improvement of Selberg's sieve method I" (PDF). Acta Arithmetica. XI: 217–240. ISSN 0065-1036. Zbl 0128...

the original on 8 April 2022. Retrieved 7 April 2019. "Remembering Atle Selberg, 1917–2007" (PDF). Ams.org. Archived (PDF) from the original on 23 November...

This is the case for small sieves (in particular, some combinatorial sieves such as the Brun sieve) rather than for large sieves; the study of the latter...

function S(t) changes sign. Earlier similar results were obtained by Atle Selberg for the case H ≥ T 1 2 + ε . {\displaystyle H\geq T^{{\frac {1}{2}}+\varepsilon...

computations, on ENIAC. The calculations were programmed and coded by Hedvig Selberg but her work was only acknowledged at the end of the paper, similarly as...

Gamburd, Alexander; Sarnak, Peter. "Generalization of Selberg's 3/16 theorem and affine sieve". Acta Mathematica 207 (2011), number 2, pages 255–290...

Eisentrager – guitar Sandris Rutmanis – drums Kevin Rutmanis – bass guitar Shannon Selberg – vocals, bugle Production and additional personnel Steve Björklund – assistant...

using the zeta function or complex analysis were found around 1948 by Atle Selberg and by Paul Erdős (for the most part independently). In 1899, de la Vallée...

70 Mu=PI(SQRT(24*N-1)/6) 80 CLR S 90 FOR K=1 TO H% 100 '110 to 160 is selberg formula 110 CLR C 120 FOR L=0 TO 2*K-1 130 IF ((3*L^2+L)\2)@K=(-N)@K 140...