## On a Question Concerning the Littlewood Violations .pdf

journal contribution

posted on 19.11.2016 by John Smith#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

Riemann's prime-counting function R(x) looks good for every value of x we can compute, but in the light of Littlewood's result its superiority over li(x) is illusory: Ingram (1938) pointed out that 'for special values of x (as large as we please), the one approximation will deviate as widely as the other from the true value'. This note introduces a type of prime-counting function that is always better than li(x)...