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On various mean values of Dirichlet L-functions

Takuya Okamoto, Tomokazu Onozuka (2015)

Acta Arithmetica

We give a method of obtaining explicit formulas for various mean values of Dirichlet L-functions which are expressed in terms of the Riemann zeta-function, the Euler function and Jordan's totient functions. Applying those results to mean values of Dirichlet L-functions, we also give an explicit formula for certain mean values of double Dirichlet L-functions.

Ordre de grandeur de L ( 1 , χ ) et de L ' ( 1 , χ )

Jean-René Joly, Claude Moser (1979)

Annales de l'institut Fourier

On étudie sommairement la distribution des valeurs de L ' ( 1 , χ ) ( χ : caractère de Dirichlet primitif réel) et on constate qu’on a en général L ' ( 1 , χ ) < π 2 / 6 ; on démontre par ailleurs que si L ' ( 1 , χ ) < ( π 2 / 6 ) - ϵ , alors L ( 1 , χ ) > c ( ϵ ) / log k ( k : conducteur de χ ; c ( ϵ ) : constante positive effectivement calculable.

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