<p>From the reviews:</p>
<p></p>
<p>"This book presents recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. … In this book the author proves universality for polynomial Euler products. … is written in a narrative and reader friendly language. The author gives many examples, presents main hypotheses and problems in the recent theory of universality. There is a large bibliography of 372 entries. The book is recommended for everybody wanting to see the current panorama of the universality theory.” (Ramunas Garunkštis, Zentralblatt MATH, Vol. 1130 (8), 2008)</p>
<p>"The book consists of 13 chapters with an appendix describing the history of universality. … In summary, this is a valuable set of lecture notes ideally suited for the researcher in analytic number theory." (M. Ram Murty, Mathematical Reviews, Issue 2008 m)</p>

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann's hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors' approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
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Universality has a strong impact on the zero-distribution: Riemann's hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. This title presents the results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality.
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Dirichlet Series and Polynomial Euler Products.- Interlude: Results from Probability Theory.- Limit Theorems.- Universality.- The Selberg Class.- Value-Distribution in the Complex Plane.- The Riemann Hypothesis.- Effective Results.- Consequences of Universality.- Dirichlet Series with Periodic Coefficients.- Joint Universality.- L-Functions of Number Fields.
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Includes supplementary material: sn.pub/extras
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Produktdetaljer

ISBN
9783540265269
Publisert
2007-06-06
Utgiver
Vendor
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter

Biographical note

Career details of the author:

1996-1999: assistant of Prof. G.J. Rieger at Hanover University

1999: PhD at Hanover University under supervision of Prof. Dr. G.J. Rieger

1999-2004: assistant of Prof. Dr. W. Schwarz and Prof. Dr. J. Wolfart at Frankfurt University

2004: Habilitation at Frankfurt University (venia legendi)

2004-today: ‘Ramon y Cajal’-investigador at Universidad Autonoma de Madrid (research fellow)