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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Originally Posted by raheel88

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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I'm not sure but probably because Riemann only used this transform for one function, whereas Mellin defined it for all functions.

good point!

In math history there's a number of cases where credit should have gone to someone else.

@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!

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