Titlebook: Value-Distribution of L-Functions; J?rn Steuding Book 2007 Springer-Verlag Berlin Heidelberg 2007 L-functions.Nevanlinna theory.Probabilit

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Dirichlet Series with Periodic Coefficients,lass of Dirichlet series includes Dirichlet .-functions, but in general these functions do not have an Euler product; anyway, we shall denote them by .(.). Such Dirichlet series are rather simple objects which have the advantage that many computations can be done explicitly. We prove universality fo

Anthrp

Joint Universality,ous uniform approximation, a topic invented by Voronin [362, 364]. Of course, such a result cannot hold for an arbitrary family of .-functions: e.g., .(.) and .(.). cannot be jointly universal. The .-functions need to be sufficiently independent to possess this joint universality property. We formul

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-Functions of Number Fields,. Further, we shall briefly discuss the arithmetic axioms in the definition of . with respect to the Langlands program. We give only a sketch of the analytic theory of all these .-functions and refer to Bump et al. [47] for further details. For details from algebraic number theory we refer to Heilbr

桉樹

ALIEN

Dirichlet Series with Periodic Coefficients,r Dirichlet series attached to non-multiplicative periodic functions subject to some side restrictions. This leads to an interesting zero-distribution which is rather different to the one of Dirichlet .-functions. The results of this chapter are due to Steuding [340, 342, 343].

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Joint Universality,ate sufficient conditions for a family of .-functions in order to be jointly universal and give examples when these conditions are fulfilled; for instance, Dirichlet .-functions to pairwise non-equivalent characters (this is an old result of Voronin) or twists of .-functions in the Selberg class subject to some condition on uniform distribution.

綠州

ANN

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Interlude: Results from Probability Theory,h course in probability theory. In Sect. 3.3 we present Denjoy‘s heuristic probabilistic argument for the truth of Riemann‘s hypothesis. Finally, in Sect. 3.7, we introduce the universe for our later studies on universality, the space of analytic functions, and state some of its properties, following Conway [62] and Laurin?ikas [186].

向外才掩飾

Limit Theorems,ntext; however, with respect to later applications, there is no need to introduce a further class. We follow the presentation of Laurin?ikas [187, 188] (functions in . form a subclass of Matsumoto zeta-functions considered herein). Besides, we refer the interested reader to Laurin?ikas‘ survey [185] and his monograph [186].