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Zeta Functions Over Zeros of Zeta Functions 2010 Edition
Contributor(s): Voros, André (Author)

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 ISBN: 3642052029     ISBN-13: 9783642052026
Publisher: Springer
OUR PRICE: $47.45  

Binding Type: Paperback
Published: December 2009
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Click for more in this series: Lecture Notes Of The Unione Matematica Italiana
Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Mathematics | Mathematical Analysis
- Mathematics | Functional Analysis
Dewey: 515
LCCN: 2009940924
Series: Lecture Notes Of The Unione Matematica Italiana
Physical Information: 0.39" H x 6.14" W x 9.21" L (0.59 lbs) 163 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
In the Riemann zeta function ?(s), the non-real zeros or Riemann zeros, denoted ?, play an essential role mainly in number theory, and thereby g- erate considerable interest. However, they are very elusive objects. Thus, no individual zero has an analytically known location; and the Riemann - pothesis, which states that all those zeros should lie on the critical line, i.e., 1 haverealpart, haschallengedmathematicianssince1859(exactly150years 2 ago). For analogous symmetric sets of numbers{v}, such as the roots of a k polynomial, the eigenvalues of a ?nite or in?nite matrix, etc., it is well known that symmetric functions of the{v} tend to have more accessible properties k than the individual elements v . And, we ?nd the largest wealth of explicit k properties to occur in the (generalized) zeta functions of the generic form 's Zeta(s, a)= (v +a) k k (with the extra option of replacing v here by selected functions f(v )). k k Not surprisingly, then, zeta functions over the Riemann zeros have been considered, some as early as 1917.What is surprising is how small the lite- ture on those zeta functions has remained overall.We were able to spot them in barely a dozen research articles over the whole twentieth century and in none ofthebooks featuring the Riemannzeta function. So the domainexists, but it has remained largely con?dential and sporadically covered, in spite of a recent surge of interest. Could it then be that those zeta functions have few or uninteresting pr- erties?Inactualfact, theirstudyyieldsanabundanceofquiteexplicitresults.
 
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