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

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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\alpha1. \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). 
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     author = {V. I. Vasyunin},
     title = {On a system of step functions},
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     volume = {262},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a1/}
}
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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/