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Math Help - Riemann's Transform?

  1. #1
    Junior Member raheel88's Avatar
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    Riemann's Transform?

    In his 1859 paper, Riemann discussed what is today known as the Inverse Mellin Transform, in orderto obtain his explicit formula for the prime counting function.

    If this is the case, why hasn't the transform been credited to Riemann's name, as Mellin was only 5 years old at the time of publication of "On the Number of Primes..."?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by raheel88 View Post
    In his 1859 paper, Riemann discussed what is today known as the Inverse Mellin Transform, in orderto obtain his explicit formula for the prime counting function.

    If this is the case, why hasn't the transform been credited to Riemann's name, as Mellin was only 5 years old at the time of publication of "On the Number of Primes..."?
    I'm not sure but probably because Riemann only used this transform for one function, whereas Mellin defined it for all functions.
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  3. #3
    Junior Member raheel88's Avatar
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    good point!
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  4. #4
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    Comment

    In math history there's a number of cases where credit should have gone to someone else.
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  5. #5
    Junior Member raheel88's Avatar
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    @wonderboy1953

    I know...this happens quite alot. This case particularly caught my eye because I'm studying Riemann's Paper as part of my course, and we keep referring to the Mellin Transform and Inverse Mellin Transform...and I'm thinking, 'surely Riemann should get credit for this?'

    He was really intuitive and alot of the steps in his paper are done without much explanation or proof, so that could be why he didn't get much recognition...plus, his hypothesis kind of overshadowed his transform!
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  6. #6
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    I'm willing to bet you that...

    Gauss should receive the credit for many theorems that others have gotten credit for.
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