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Zbl 1138.11337
Jousse, Nicolas
A problem of continuity linked to the Riemann hypothesis. (Étude d'un problème de continuité lié à l'hypothèse de Riemann.) (French)
[J] Ann. Inst. Fourier 55, No. 4, 1373-1410 (2005). ISSN 0373-0956; ISSN 1777-5310/e

Summary: This work is devoted to a problem linked to the Beurling-Nyman's criterion about the Riemann hypothesis. We study the continuity of the projection of the characteristic function of $(0,1)$ on a subspace of the square-integrable functions generated by dilated functions of the fractional part function. More generally, if $y$ is a vector belonging to a Hilbert space $H$, we study the function, which maps any closed and convex subspace $C$ of $H$ to the orthogonal projection of $y$ on $C$.

MSC 2000:: *11M26 Nonreal zeros of zeta(s) and L(s,chi)
46C05 Geometry and topology of inner product spaces
46E15 Banach spaces of functions defined by smoothness properties
47B38 Operators on function spaces

Keywords: Riemann hypothesis; Beurling-Nyman criterion; dilated functions; continuity; projection

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Zentralblatt MATH Berlin [Germany]