Zeros of Sections of Power Series, A. Edrei; E. B. Saff; R. S. Varga

Автор: Andr? Voros
Название: Zeta Functions over Zeros of Zeta Functions
ISBN: 3642052029 ISBN-13(EAN): 9783642052026
Издательство: Springer
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Описание: 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.

Автор: Andrei Osipov; Vladimir Rokhlin; Hong Xiao
Название: Prolate Spheroidal Wave Functions of Order Zero
ISBN: 1461482585 ISBN-13(EAN): 9781461482581
Издательство: Springer
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Описание: A complete resource on theory and computation, this book will be of interest to a range of practitioners, from mathematicians interested in prolate spheroidal wave functions as an analytical tool to electrical engineers designing filters and antennas.

Автор: Andrei Osipov; Vladimir Rokhlin; Hong Xiao
Название: Prolate Spheroidal Wave Functions of Order Zero
ISBN: 1489978658 ISBN-13(EAN): 9781489978653
Издательство: Springer
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Описание: A complete resource on theory and computation, this book will be of interest to a range of practitioners, from mathematicians interested in prolate spheroidal wave functions as an analytical tool to electrical engineers designing filters and antennas.

Автор: Peter Kravanja; Marc Van Barel
Название: Computing the Zeros of Analytic Functions
ISBN: 3540671625 ISBN-13(EAN): 9783540671626
Издательство: Springer
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Описание: This guide treats four major problems within computational complex analysis in a unified way: computing the zeros and their multiplicities in analytic functions; locating clusters of zeros; computing zeros and poles of meromorphic functions; and solving analytic equations.