Displaying similar documents to “Zeros of Padé approximants for some classes of functions”

Flows of Mellin transforms with periodic integrator

Titus Hilberdink (2011)

Journal de Théorie des Nombres de Bordeaux

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We study Mellin transforms N ^ ( s ) = ∫ 1 - ∞ x - s d N ( x ) for which N ( x ) - x is periodic with period 1 in order to investigate ‘flows’ of such functions to Riemann’s ζ ( s ) and the possibility of proving the Riemann Hypothesis with such an approach. We show that, excepting the trivial case where N ( x ) = x , the supremum of the real parts of the zeros of any such function is at least 1 2 . We investigate a particular flow of such functions { N λ ^ } λ ≥ 1 which converges locally uniformly to ζ ( s ) as λ → 1 , and show that they exhibit features similar...