The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “A multiple sum involving the Möbius function.”

Gaps between zeros of the derivative of the Riemann ξ -function

Hung Manh Bui (2010)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of ξ ( s ) . We prove that a positive proportion of gaps are less than 0 . 796 times the average spacing and, in the other direction, a positive proportion of gaps are greater than 1 . 18 times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than 0 . 7203 ( 1 . 5 , respectively).

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 ) : = 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...

Palindromic powers.

Hernández, Santos Hernández, Luca, Florian (2006)

Revista Colombiana de Matemáticas

Similarity:

On Bombieri's asymptotic sieve

John Friedlander, Henryk Iwaniec (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity: