Displaying similar documents to “Products of integral-type and composition operators between generally weighted Bloch spaces.”

Palindromic powers.

Hernández, Santos Hernández, Luca, Florian (2006)

Revista Colombiana de Matemáticas

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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 ) : = ∑ d | n d < e γ n log log n is satisfied for n ≥ 5041 , where γ denotes the Euler(-Mascheroni) constant. We show by elementary methods that if n ≥ 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...

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 ≥ 2 . In a well-known paper , 20, 1077–1092 (1971) Moser found the smallest value of K such that sup ∫ Ω exp f ( x ) K n / ( n - 1 ) : f ∈ W 0 1 , n ( Ω ) , ∥ ∇ f ∥ L n ≤ 1 < ∞ . 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.