Displaying similar documents to “On the growth of analytic functions represented by Dirichlet series”

Extremal values of Dirichlet L -functions in the half-plane of absolute convergence

Jörn Steuding (2004)

Journal de Théorie des Nombres de Bordeaux

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We prove that for any real θ there are infinitely many values of s = σ + i t with σ → 1 + and t → + ∞ such that ℜ { exp ( i θ ) log L ( s , χ ) } ≥ log log log log t log log log log t + O ( 1 ) . The proof relies on an effective version of Kronecker’s approximation theorem.

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 -...