Selberg's sieve method (continued)

2010 ◽  
pp. 43-66
Author(s):  
Harold G. Diamond ◽  
H. Halberstam ◽  
William F. Galway
Keyword(s):  
Sieve Method ◽  
Selberg’S Sieve Method ◽  
Selberg's Sieve

Selberg's sieve method

2010 ◽  
pp. 13-18
Author(s):  
Harold G. Diamond ◽  
H. Halberstam ◽  
William F. Galway
Keyword(s):  
Sieve Method ◽  
Selberg’S Sieve Method ◽  
Selberg's Sieve

Selberg's sieve with weights

Mathematika ◽  
1969 ◽  
Vol 16 (1) ◽  
pp. 1-22 ◽  
Author(s):  
H.-E. Richert
Keyword(s):  
Selberg's Sieve

scholarly journals Selberg's sieve estimate with a one sided hypothesis

1982 ◽  
Vol 41 (3) ◽  
pp. 281-289 ◽  
Author(s):  
Daniel Rawsthorne
Keyword(s):  
Selberg's Sieve

scholarly journals The Barban-Vehov Theorem in Arithmetic Progressions

2019 ◽  
Author(s):  
V Kumar Murty
Keyword(s):  
Asymptotic Formula ◽  
Arithmetic Progression ◽  
Upper Bound ◽  
Arithmetic Progressions ◽  
Mean Square ◽  
Titchmarsh Theorem ◽  
International Audience ◽  
The Mean ◽  
Selberg's Sieve

International audience A result of Barban-Vehov (and independently Motohashi) gives an estimate for the mean square of a sequence related to Selberg's sieve. This upper bound was refined to an asymptotic formula by S. Graham in 1978. In 1992, I made the observation that Graham's method can be used to obtain an asymptotic formula when the sum is restricted to an arithmetic progression. This formula immediately gives a version of the Brun-Titchmarsh theorem. I am taking the occasion of a volume in honour of my friend S. Srinivasan to revisit and publish this observation in the hope that it might still be of interest.

scholarly journals An improvement of Selberg's sieve method I

1965 ◽  
Vol 11 (2) ◽  
pp. 217-240 ◽  
Author(s):  
W. Jurkat ◽  
H. Richert
Keyword(s):  
Sieve Method ◽  
Selberg’S Sieve Method ◽  
Selberg's Sieve

scholarly journals Explicit counting of ideals and a Brun–Titchmarsh inequality for the Chebotarev density theorem

2019 ◽  
Vol 15 (05) ◽  
pp. 883-905 ◽  
Author(s):  
Korneel Debaene
Keyword(s):  
Arithmetic Progression ◽  
Number Fields ◽  
Field Extension ◽  
Density Theorem ◽  
Explicit Estimate ◽  
Chebotarev Density Theorem ◽  
Set Up ◽  
Selberg's Sieve

We prove a bound on the number of primes with a given splitting behavior in a given field extension. This bound generalizes the Brun–Titchmarsh bound on the number of primes in an arithmetic progression. The proof is set up as an application of Selberg’s Sieve in number fields. The main new ingredient is an explicit counting result estimating the number of integral elements with certain properties up to multiplication by units. As a consequence of this result, we deduce an explicit estimate for the number of ideals of norm up to [Formula: see text].

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