Mean value of Piltz' function over integers free of large prime factors.

Nyandwi, Servat

Displaying similar documents to “Mean value of Piltz' function over integers free of large prime factors.”

Products of integral-type and composition operators between generally weighted Bloch spaces.

Li, Haiying, Ma, Tianshui (2011)

Acta Mathematica Universitatis Comenianae. New Series

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On Robin’s criterion for the Riemann hypothesis

YoungJu Choie, Nicolas Lichiardopol, Pieter Moree, Patrick Solé (2007)

Journal de Théorie des Nombres de Bordeaux

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Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality $σ (n) : = \sum_{d | n} d < e^{γ} n log log n$ is satisfied for $n \geq 5041$ , where $γ$ denotes the Euler(-Mascheroni) constant. We show by elementary methods that if $n \geq 37$ does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that $n$ must be divisible by a fifth power $> 1$ . As consequence we obtain that RH holds true iff every natural number divisible by...

Palindromic powers.

Hernández, Santos Hernández, Luca, Florian (2006)

Revista Colombiana de Matemáticas

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Another relation between π, e, γ and ζ(n).

Luis J. Boya (2008)

RACSAM

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Perfect powers in the summatory function of the power tower

Florian Luca, Diego Marques (2010)

Journal de Théorie des Nombres de Bordeaux

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Let ${(a_{n})}_{n \geq 1}$ be the sequence given by $a_{1} = 1$ and $a_{n} = n^{a_{n - 1}}$ for $n \geq 2$ . In this paper, we show that the only solution of the equation $a_{1} + \dots + a_{n} = m^{l}$ is in positive integers $l > 1, m$ and $n$ is $m = n = 1$ .

A sharp form of an embedding into multiple exponential spaces

Robert Černý, Silvie Mašková (2010)

Czechoslovak Mathematical Journal

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Let $Ω$ be a bounded open set in $ℝ^{n}$ , $n \geq 2$ . In a well-known paper , 20, 1077–1092 (1971) Moser found the smallest value of $K$ such that $sup \{\int_{Ω} exp ({(\frac{|f (x)|}{K})}^{n / (n - 1)}) : f \in W_{0}^{1, n} (Ω), {∥ \nabla f ∥}_{L^{n}} \leq 1\} < \infty .$ We extend this result to the situation in which the underlying space $L^{n}$ is replaced by the generalized Zygmund space $L^{n} {log}^{n - 1} L {log}^{α} log L$ $(α < n - 1)$ , the corresponding space of exponential growth then being given by a Young function which behaves like $exp (exp (t^{n / (n - 1 - α)}))$ for large $t$ . We also discuss the case of an embedding into triple and other multiple exponential cases.

Integer sequences, functions of slow increase, and the Bell numbers.

Jakimczuk, Rafael (2011)

Journal of Integer Sequences [electronic only]

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