Displaying similar documents to “On a new method in the analysis with applications”

Upper bounds for the density of universality. II

Jörn Steuding (2005)

Acta Mathematica Universitatis Ostraviensis

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We prove explicit upper bounds for the density of universality for Dirichlet series. This complements previous results [15]. Further, we discuss the same topic in the context of discrete universality. As an application we sharpen and generalize an estimate of Reich concerning small values of Dirichlet series on arithmetic progressions in the particular case of the Riemann zeta-function.

Zeros and poles of Dirichlet series

Enrico Bombieri, Alberto Perelli (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Under certain mild analytic assumptions one obtains a lower bound, essentially of order r , for the number of zeros and poles of a Dirichlet series in a disk of radius r . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.