Gaps between zeros of the derivative of the Riemann $\xi $-function

Hung Manh Bui

Displaying similar documents to “Gaps between zeros of the derivative of the Riemann $ξ$ -function”

On a problem of Fujii concerning Riemann's $ζ$ -function.

Puchta, J.-C. (2001)

Acta Mathematica Universitatis Comenianae. New Series

Similarity:

On certain sums over ordinates of zeta-zeros

A. Ivić (2001)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Similarity:

On Robin’s criterion for the Riemann hypothesis

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

Journal de Théorie des Nombres de Bordeaux

Similarity:

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...

A multiple sum involving the Möbius function.

Motohashi, Yoichi (2004)

Publications de l'Institut Mathématique. Nouvelle Série

Similarity:

Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Mertens’ product formula asserts that $\prod_{p \leq x} (1 - \frac{1}{p}) log x \to e^{- γ}$ as $x \to \infty$ . Calculation shows that the right side of the formula exceeds the left side for $2 \leq x \leq 10^{8}$ . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on $π (x) - li x$ , this and a complementary inequality might change their sense for sufficiently large values of $x$ . We show this to be the case.

An arithmetic function arising from Carmichael’s conjecture

Florian Luca, Paul Pollack (2011)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $φ$ denote Euler’s totient function. A century-old conjecture of Carmichael asserts that for every $n$ , the equation $φ (n) = φ (m)$ has a solution $m \neq n$ . This suggests defining $F (n)$ as the number of solutions $m$ to the equation $φ (n) = φ (m)$ . (So Carmichael’s conjecture asserts that $F (n) \geq 2$ always.) Results on $F$ are scattered throughout the literature. For example, Sierpiński conjectured, and Ford proved, that the range of $F$ contains every natural number $k \geq 2$ . Also, the maximal order of $F$ has been investigated by Erdős and Pomerance....

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

Luis J. Boya (2008)

RACSAM

Similarity:

Displaying similar documents to “Gaps between zeros of the derivative of the Riemann ξ -function”

On a problem of Fujii concerning Riemann's ζ -function.

On certain sums over ordinates of zeta-zeros

On Robin’s criterion for the Riemann hypothesis

A multiple sum involving the Möbius function.

Oscillation of Mertens’ product formula

An arithmetic function arising from Carmichael’s conjecture

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

Displaying similar documents to “Gaps between zeros of the derivative of the Riemann $ξ$ -function”

On a problem of Fujii concerning Riemann's $ζ$ -function.