Wiener Ikehara Theorem
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High Quality Content by WIKIPEDIA articles! The Wiener Ikehara theorem can be used to prove the prime number theorem (PNT) (Chandrasekharan, 1969). It was proved by Norbert Wiener and his student Shikao Ikehara in 1932. It is an example of a Tauberian theorem.In mathematics, abelian and tauberian theorems relate to the meaningful assignment of a value as the "sum" of a class of divergent series. A large number of methods have been proposed for the summation of such series, generally taking the form of some linear functional L with domain contained in some space S of numerical sequences. That i...
High Quality Content by WIKIPEDIA articles! The Wiener Ikehara theorem can be used to prove the prime number theorem (PNT) (Chandrasekharan, 1969). It was proved by Norbert Wiener and his student Shikao Ikehara in 1932. It is an example of a Tauberian theorem.In mathematics, abelian and tauberian theorems relate to the meaningful assignment of a value as the "sum" of a class of divergent series. A large number of methods have been proposed for the summation of such series, generally taking the form of some linear functional L with domain contained in some space S of numerical sequences. That is, firstly, a useful method for attributing a sum to a series that doesn't converge should at least be linear. Secondly, the sequence of partial sums of the series is considered, which is an equivalent way of presenting it.
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