Good variation theory (v 23/12/2015)

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.

Conjecture de comparaison, 2015

In this note in french I propose to tackle RH using function of good variation and a comparison method.

Good mollifiers for the Ingham function, 2015

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.

A tauberian approach to RH, 2011

It was my first tentative to approach RH witht good variation theory. Many wrong claims but historically the first insights were illuminating.

Dirichlet divisors problem=Gauss circle problem, 2013

In this note I tried to show that both problem are equivalent using a conjecture on an intrinsic property of the fractional part function.