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Zeta Functions Over Zeros of Zeta Functions by Andre Voros - Paperback
219.45 AED

Zeta Functions Over Zeros of Zeta Functions by Andre Voros - Paperback

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Category Type
Mathematics
ISBN
9783642052026
Author
Andre Voros
Publisher
Springer
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, ...

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PRODUCT INFORMATION

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    Specifications

    Category Type
    Mathematics
    ISBN
    9783642052026
    Languages
    English
    Item EAN
    2724437183911
    People
    Author
    Andre Voros
    Category Type
    Mathematics
    ISBN
    9783642052026
    Languages
    English
    Item EAN
    2724437183911
    People
    Author
    Andre Voros
    People
    Publisher
    Springer
    Technical Information
    Binding
    Paperback
    Languages and countries
    Book Language
    English
    Read more
  •  

    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 -

    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.

    Product Features:
    • Category: Mathematics
    • Binding: Paperback
    • Language of Text: English
    • Author(s): Andre Voros
    • Publisher: Springer
    • ISBN: 9783642052026
    • Number of Pages: 163
    • Dimensions: 9.21 x 6.14 x 0.39 inches
 

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