Offers recent results in the value-distribution theory of L-functions
Universality is proved for polynomial Euler products
The authors offer the conjecture that all reasonable L-functions are universal
Includes supplementary material: sn.pub/extras
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)
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.
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.
From the reviews:
"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)
"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)
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.
From the reviews:
"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 Garunkstis, Zentralblatt MATH, Vol. 1130 (8), 2008)
"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)
Über den Autor
Career details of the author:n1996-1999: assistant of Prof. G.J. Rieger at Hanover Universityn1999: PhD at Hanover University under supervision of Prof. Dr. G.J. Riegernn1999-2004: assistant of Prof. Dr. W. Schwarz and Prof. Dr. J. Wolfart at Frankfurt Universityn2004: Habilitation at Frankfurt University (venia legendi)nn2004-today: `Ramon y Cajal-investigador at Universidad Autonoma de Madrid (research fellow)
Inhaltsverzeichnis
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.
Klappentext
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.
Includes supplementary material: sn.pub/extras
