Displaying similar documents to “On an estimate of Walfisz and Saltykov for an error term related to the Euler function”

On the fractional parts of x / n and related sequences. II

Bahman Saffari, R. C. Vaughan (1977)

Annales de l'institut Fourier

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As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of x h ( x ) where h is an arithmetical function (namely h ( n ) = 1 / n , h ( n ) = log n , h ( n ) = 1 / log n ) and n is an integer (or a prime order) running over the interval [ y ( x ) , x ) ] . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.

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 { 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.