Thesis (M. Phil.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 85-87).

Thesis (Ph. D.)--University of Massachusetts Amherst, 2009. / Includes bibliographical references (p. 127-128). Print copy also available.

Thesis (M.A.) in Mathematics--University of Maine, 2005. / Includes vita. Includes bibliographical references (leaves 84-87).

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Orientador: Ketty Rezende / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-11T23:47:35Z (GMT). No. of bitstreams: 1 Almeida_Iamakauede_M.pdf: 1614719 bytes, checksum: 7d907bd04283179d264458b8a701be2b (MD5) Previous issue date: 2000 / Resumo: Não informado / Abstract: Not informed / Mestrado / Mestre em Matemática

We consider the entire function [formula omitted] whose set of zeros includes the zeros of [formula omitted](s), expand it in an everywhere converging Maclauring series [formula omitted] Then we determine analytic expressions for the coefficients a[formula omitted] which will enable us to proceed with the numerical evaluation of some of these coefficients. To achieve this, we define an operator D[formula omitted] acting on a restricted class of power series and which we call the zeta operator. Using the operator D[formula omitted], we are able to express the coefficients a[formula omitted] as infinite n-dimensional integrals. Numerical values for the coefficients a₀ and a₁ are easily determined. For a₂ and a₃, we transform the multidimensional integrals into products of single integrals and obtain infinite series expressions for these coefficients. Although our method can also be used on the following coefficients, it turns out that the work involved to obtain an expression leading to a practical numerical evaluation of a₄, a₅, …,seems prohibitive at this stage. We then proceed with the numerical computation of a₂ and a₃ and we use these coefficients to calculate the sums of reciprocals of the zeros of [formula omitted](s) in the critical strip. Finally, assuming Riemann hypothesis, we calculate a few other quantities which may prove to be of interest. / Science, Faculty of / Computer Science, Department of / Graduate

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A. Speiser'is parodė, kad Riemann'o hipotezė yra ekvivalenti tam, kad Riemann'o dzeta funkcijos išvestinė neturi netrivialių nulių į kairę nuo kritinės tiesės. Kiekybinis šio fakto rezultatas buvo pasiektas N. Levinsono ir H. Montgomerio. Šie rezultatai buvo apibendrinti daugeliui dzeta funkcijų, kurioms tikimasi, kad Riemann'o hipotezė galioja. Šiame darbe mes apibendriname Speiser'io ekvivalentą dzeta-funkcijoms. Mes tiriame sąryšį tarp netrivialių nulių išplėstinės Selbergo klasės funkcijoms ir jų išvestinėms šiame regione. Šiai klasei priklauso ir funkcijos, kurioms Riemann'o hipotezė neteisinga. Kaip pavyzdį, mes skaitiniu būdu tiriame sąryšius tarp Dirichlet L-funkcijų ir jų išvestinių tiesinių kombinacijų. / A. Speiser showed that the Riemann hypothesis is equivalent to the absence of non-trivial zeros of the derivative of the Riemann zeta-function left of the critical line. The quantitative version of this result was obtained by N. Levinson and H. Montgomery. This result (or the quantitative version of this result proved by N. Levinson and H. Montgomery) were generalized for many zeta-functions for which the Riemann hypothesis is expected. Here we generalize the Speiser equivalent for zeta-functions. We also investigate the relationship between the on-trivial zeros of the extended Selberg class functions and of their derivatives in this region. This class contains zeta functions for which Riemann hypothesis is not true. As an example, we study the relationship between the trajectories of zeros of linear combinations of Dirichlet $L$-functions and of their derivatives computationally.

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Thesis (Ph. D.)--Institute of Paper Science and Technology, 1989. / Bibliography: leaves 94-100.