Timeline for Density of numbers whose prime factors belong to given arithmetic progressions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 2, 2017 at 18:05 | comment | added | Daniel Loughran | The constant in the closely related case of representations of integers by binary quadratic forms can be found in: Brink, Moree, Osburn - Principal forms $x^2+ny^2$ representing many integers. | |
| Apr 2, 2017 at 18:03 | comment | added | Daniel Loughran | It is quite easy to write down the constant $C$ explicitly. One can write the associated Dirichlet series in terms of Dirichlet $L$-functions. One then obtains the asymptotic formula and thus $C$ via a Tauberian theorem ($C$ will be written in terms of special values of Dirichlet $L$-functions, which can be "calculated" using the class number formula). These methods are all explained very well in the cited paper of Serre; I would very much recommend that you study it. | |
| Apr 2, 2017 at 16:58 | comment | added | Tian An | I'll accept the answer, though I realize now that what I was really looking for was this constant $C$ explicitly. I couldn't find this exact derivation in Landau.. | |
| Apr 2, 2017 at 16:57 | vote | accept | Tian An | ||
| Mar 21, 2017 at 11:08 | history | answered | Daniel Loughran | CC BY-SA 3.0 |