Geodesic
On a system of step functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 49-70 
V. I. Vasyunin. On a system of step functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 49-70. http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a1/
@article{ZNSL_1999_262_a1,
     author = {V. I. Vasyunin},
     title = {On a system of step functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {49--70},
     year = {1999},
     volume = {262},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a1/}
}
TY  - JOUR
AU  - V. I. Vasyunin
TI  - On a system of step functions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1999
SP  - 49
EP  - 70
VL  - 262
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a1/
LA  - ru
ID  - ZNSL_1999_262_a1
ER  - 
%0 Journal Article
%A V. I. Vasyunin
%T On a system of step functions
%J Zapiski Nauchnykh Seminarov POMI
%D 1999
%P 49-70
%V 262
%U http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a1/
%G ru
%F ZNSL_1999_262_a1

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is well-known that the Riemann hypothesis is equivalent to the assertion that the identity function belongs to the linear span in $L^2(0,1)$ of the following function set \begin{equation} \left[\frac\alpha x\right]-\alpha\left[\frac1x\right], \qquad 0<\alpha<1. \tag{1} \end{equation} A step is presented in describing the set of all idempotents representable as a finite sum of functions of the form (1).