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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Editorial Reviews
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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)
About the Author
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)
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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joint universality, universality theorem, normality conjecture, inhomogeneous diophantine approximation, pair correlation conjecture, positive lower density, analytic landscape, connected complement, critical strip, cuspidal automorphic representation, strong universality, full modular group, automorphic representations, density hypothesis, prime number theorem, unique prime factorization, rational parameters, series satisfying, universality property, cusp forms, analytic behaviour, quadratic number fields, density theorem, critical line, functional equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Dirichlet L-functions, Artin L-functions, Hecke L-functions, Riemann-von Mangoldt, Dense Sets, Grand Riemann, Rankin-Selberg L-function, The Linnik-Ibragimov Conjecture, The Positive-Density Method, Twisted L-Functions, Big Picard, Sums Over New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
joint universality, universality theorem, normality conjecture, inhomogeneous diophantine approximation, pair correlation conjecture, positive lower density, analytic landscape, connected complement, critical strip, cuspidal automorphic representation, strong universality, full modular group, automorphic representations, density hypothesis, prime number theorem, unique prime factorization, rational parameters, series satisfying, universality property, cusp forms, analytic behaviour, quadratic number fields, density theorem, critical line, functional equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Dirichlet L-functions, Artin L-functions, Hecke L-functions, Riemann-von Mangoldt, Dense Sets, Grand Riemann, Rankin-Selberg L-function, The Linnik-Ibragimov Conjecture, The Positive-Density Method, Twisted L-Functions, Big Picard, Sums Over New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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