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

Y.-F. S. Pétermann

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

On sums of sequences of integers, I

A. Balog, András Sárközy (1984)

Acta Arithmetica

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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.

The distribution of values of the Euler function

Paul Bateman (1972)

Acta Arithmetica

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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 $σ \to 1 +$ and $t \to + \infty$ such that $ℜ {exp (i θ) log L (s, χ)} \geq log \frac{log log log t}{log log log log t} + O (1) .$ The proof relies on an effective version of Kronecker’s approximation theorem.

The Dirichlet series of $ζ (s) ζ^{α} (s + 1) f (s + 1)$ : On an error term associated with its coefficients

U. Balakrishnan, Y.-F. S. Pétermann (1996)

Acta Arithmetica

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A simple proof of the mean fourth power estimate for $ζ (\frac{1}{2} + i t)$ and $L (\frac{1}{2} + i t, χ)$

K. Ramachandra (1974)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On the difference between perfect powers

Jan Turk (1986)

Acta Arithmetica

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

On sums of sequences of integers, I

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

The distribution of values of the Euler function

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

The Dirichlet series of ζ ( s ) ζ α ( s + 1 ) f ( s + 1 ) : On an error term associated with its coefficients

A simple proof of the mean fourth power estimate for ζ ( 1 2 + i t ) and L ( 1 2 + i t , χ )

On the difference between perfect powers

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

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

The Dirichlet series of $ζ (s) ζ^{α} (s + 1) f (s + 1)$ : On an error term associated with its coefficients

A simple proof of the mean fourth power estimate for $ζ (\frac{1}{2} + i t)$ and $L (\frac{1}{2} + i t, χ)$