Talk:Linnik's theorem

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[edit] Linnik's constant

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

"there exist positive c and L such that: p(a,d) < c d^{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)