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Study of the multiplicative autocorrelation of the fractional part function. (Étude de l’autocorrélation multiplicative de la fonction ‘partie fractionnaire’.) (French) Zbl 1173.11343
The authors study the function \[ A(\lambda):=\int_0^\infty\{t\}\{\lambda t\}\frac{dt}{t^2},\quad \lambda>0, \] which can be used to reformulate the Riemann hypothesis. They prove that this function has a strict local maximum at every rational point and that its Mellin transform is \[ -\frac{\zeta(-s)\zeta(s+1)}{s(s+1)}. \]

11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11L99 Exponential sums and character sums
Full Text: DOI
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