Displaying similar documents to “Extremal values of Dirichlet L -functions in the half-plane of absolute convergence”

On entire functions represented by Dirichlet series. IV

Pawan Kumar Kamthan (1966)

Annales de l'institut Fourier

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Dans cet article, on démontre quelques théorèmes nouveaux relatifs aux fonctions entières f ( s ) sommes de séries de Dirichlet ; ces résultats sont relatifs, en particulier, aux dérivées de f ( s ) et à une généralisation de la formule de Poisson.

On an estimate of Walfisz and Saltykov for an error term related to the Euler function

Y.-F. S. Pétermann (1998)

Journal de théorie des nombres de Bordeaux

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The technique developed by A. Walfisz in order to prove (in 1962) the estimate H ( x ) ( log x ) 2 / 3 ( log log x ) 4 / 3 for the error term H ( x ) = n x φ ( n ) n - 6 π 2 x related to the Euler function is extended. Moreover, the argument is simplified by exploiting works of A.I. Saltykov and of A.A. Karatsuba. It is noted in passing that the proof proposed by Saltykov in 1960 of H ( x ) ( log x ) 2 / 3 ( log log x ) 1 + ϵ is erroneous and once corrected “only” yields Walfisz’ result. The generalizations obtained can be applied to error terms related to various classical - and less classical -...