Some problems on mean values of the Riemann zeta-function

Ivić, Aleksandar

Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 1, pp. 101-123.

On s’intéresse à des problèmes et des résultats relatifs aux valeurs moyennes de la fonction $\zeta \left(s\right)$. On étudie en particulier des valeurs moyennes de $\left|\zeta \right(\frac{1}{2}+it\left)\right|$, ainsi que le moment d’ordre $4$ de $\left|\zeta \right(\sigma +it\left)\right|$ pour $1/2<\sigma <1$.

Several problems and results on mean values of $\zeta \left(s\right)$ are discussed. These include mean values of $\left|\zeta \right(\frac{1}{2}+it\left)\right|$ and the fourth moment of $\left|\zeta \right(\sigma +it\left)\right|$ for $1/2<\sigma <1$.

Classification : Primary 11M06
Mots clés : Riemann zeta-function, mean values, asymptotic formulas

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