This note is an update of all my research related to functions of good variation since 2011. Related stuff, good and bad, is listed below.
In this note in french I described for the first time precise tauberian formulas related to the Ingham function.
In this note in french I propose to tackle RH using function of good variation and a comparison method.
I tried to explore further a mollification method to tackle RH made a conjecture on a family of mollifiers which could be good enough.
Broken harmonic functions (BHF), 2014
I introduced for the first time the concept of BHF which is a generalisation of the Ingham function and proposed a method of comparison.
Mock Liouville functions, 2014
Using functions of good varations I tried to approach RH by considering a family of functions related to the Liouville lambda function. This method appears to be useless now.
It was my first tentative to approach RH witht good variation theory. Many wrong claims but historically the first insights were illuminating.
In this note I tried to show that both problem are equivalent using a conjecture on an intrinsic property of the fractional part function.