Talk:Linnik's theorem

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Linnik's constant[edit]

How exactly is Linnik's constant defined? The article currently says:

"there exist positive c and L such that:

p(a,d)<cd^{L}\;.

... The constant L is called Linnik's constant".

The sources I have seen have similar definitions, but there exist infinitely many L satisfying the condition. Is Linnik's constant the smallest L? Or possibly the infimum of the L values if there is no smallest? Or is Linnik's constant not a fixed real number but just whichever L value is considered in a given situation and proven to satisfy the condition? PrimeHunter (talk) 04:04, 13 March 2008 (UTC)[reply]

Linnik's constant is whatever you define it to be and I have come across authors who use the definition with the infimum as well as authors who use your mentioned definition where L is not a fixed constant. T.X. (edited)

Reference [14][edit]

The article states that "It is known that L ≤ 2 for almost all integers d.[14]" but I looked over the reference [14] and couldn't find this statement. Can someone tell where the L ≤ 2-statement is proven? T.X. —Preceding unsigned comment added by 84.130.57.100 (talk) 00:42, 9 December 2008 (UTC)[reply]

"Almost all"[edit]

In the statement "L ≤ 2 for almost all integers", as an analyst I immediately take this to mean that it holds except for a set of integers of measure zero. But then the article needs to specify what measure is being used. This is particularly important since the only measure I know of on the integers is the counting measure, for which "almost all" is precisely the same as "all" (or the Lebesgue measure, which has the opposite property that all subsets of N, even N itself, are of measure zero ) . 128.40.56.75 (talk) 13:55, 27 October 2009 (UTC)[reply]

Terms in Wikipedia are often linked to an article explaining them. The quoted statement actually has a link: "L ≤ 2 for almost all integers". The article almost all includes the relevant definition for integers. PrimeHunter (talk) 22:29, 27 October 2009 (UTC)[reply]