André Voros

Zeta Functions over Zeros of Zeta Functions (eBook, PDF)

• Format: PDF

Produktdetails

• Verlag: Springer Berlin
• Erscheinungstermin: 21. November 2009
• Englisch
• ISBN-13: 9783642052033
• Artikelnr.: 37368541

Inhaltsangabe

---

Infinite Products and Zeta-Regularization.- The Riemann Zeta Function #x03B6;(): a Primer.- Riemann Zeros and Factorizations of the Zeta Function.- Superzeta Functions: an Overview.- Explicit Formulae.- The Family of the First Kind {#x2112; ( )}.- The Family of the Second Kind.- The Family of the Third Kind.- Extension to Other Zeta- and -Functions.- Application: an Asymptotic Criterion for the Riemann Hypothesis.

Rezensionen

From the reviews:

"The book is written in a pleasant style, with short chapters, each explaining a single topic. ... This book is a very timely synthesis of the results that have been scattered in the literature up to now. It gives a systematic overview and adds the discoveries of the author (with collaborators). ... this book will prove to be an important step in the further development of the subject of superzeta functions." (Machiel van Frankenhuijsen, Mathematical Reviews, Issue 2010 j)

"The book is very carefully written and presents an object of research which has been investigated for many decades but never treated in such a comprehensive manner. A valuable contribution to the field of analytic number theory." (Anton Deitmar, Zentralblatt MATH, Vol. 1206, 2011)