Darbe nagrinėjamas paprastųjų Dirichlė eilučių, turinčių polinominę Oilerio sandaugą, analizinį pratęsimą, Rymano tipo funkcinę lygtį bei tenkinančių Ramanudžano hipotezę, klasės funkcijų reikšmių pasiskirstymas. Įrodyta ribinė teorema silpnojo tikimybinių matų konvergavimo prasme šios klasės funkcijoms, meromorfinių funkcijų erdvėje pateiktas išreikštinis ribinio mato pavidalas. / The paper examines ordinary Dirichlet series with Euler product of a polynomial, analytical continuation, the Riemann-type functional equation and satisfying Ramanudžano hypothesis class distribution function values​​. Been shown to limit theorem of the weak convergence of probability measures in terms of the class functions meromorfinių functions in the explicit marginal visible form.

Zugl.: Karlsruhe, Univ., Diss., 2009 / Hergestellt on demand

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.

Thesis (Ph. D.)--Carleton University, 2001. / Includes bibliographical references (p. 141-144). Also available in electronic format on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 80-81). Available also in a digital version from Dissertation Abstracts.

Thesis (Doctoral)--Universität Bonn, 1990. / Includes bibliographical references.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2006. / Submitted by wesley oliveira leite (leite.wesley@yahoo.com.br) on 2009-11-25T16:08:33Z No. of bitstreams: 1 2006_TheoAllanDarnZapata.pdf: 585718 bytes, checksum: 6c3355de7df60627ab844ddbb518297a (MD5) / Approved for entry into archive by Joanita Pereira(joanita) on 2009-12-07T17:06:59Z (GMT) No. of bitstreams: 1 2006_TheoAllanDarnZapata.pdf: 585718 bytes, checksum: 6c3355de7df60627ab844ddbb518297a (MD5) / Made available in DSpace on 2009-12-07T17:06:59Z (GMT). No. of bitstreams: 1 2006_TheoAllanDarnZapata.pdf: 585718 bytes, checksum: 6c3355de7df60627ab844ddbb518297a (MD5) Previous issue date: 2006 / Neste trabalho estabelecemos propriedades analíticas e aritméticas de duas L- funções automór cas para o grupo modular, as de Hecke-Maass e Rankin-Selberg. A partir das quais, obtemos limitantes superiores para somas de coe cientes de formas automór cas cuspidais. ________________________________________________________________________________________ ABSTRACT / In this work we estabilish analytical and arithmetical proprieties of two auto- morphic L-functions for the modular group, those of Hecke-Maass and Rankin- Selberg. From these, we obtain upper bounds for sums of the coe cients of auto- morphic cusp forms.

Le but de cette thèse est d'étudier les zéros exceptionnels des fonctions L p-adiques de Rankin-Selberg. Autrement dit, pour un couple de formes modulaires nous étudierons l'annulation de la fonction p-adique interpolant la fonction L de Rankin-Selberg associée à ce couple. Lorsque la fonction s'annule, on exprime alors la dérivée de la fonction L p-adique en fonction de l'invariant L,des périodes p-adique et infinie et du terme principal de la fonction complexe de Rankin-Selberg. / The aim of this thesis is to study the extra zeros of the p-adic L functions of Rankin-Selberg. In other words, for a couple of modular forms we study the zeros of the p-adic function interpolating the Rankin-Selberg L function associated to this couple. When the function has a zero we express the value of the derivate in terms of the L invariant, p-adic and infinite periods and the principal term of the complex Rankin-Selberg function.

On étudie les valeurs spéciales de fonctions $L$ attachées aux formes modulaires, tordues par des caractères de Dirichlet de conducteur arbitraire. On construit des distributions à valeurs algébriques à partir de distributions à valeurs modulaires. On prouve sur ces dernières des résultats de congruence et d'admissibilité. On obtient alors les distributions scalaires en appliquant une forme linéaire, ce qui permet de montrer qu'elles vérifient elles aussi de bonnes propriétés. On établit ensuite un lien entre ces distributions scalaires et les valeurs spéciales qui nous intéressent, ce qui permet d'établir de nouvelles congruences entre elles.

We prove several inequalities involving the Fourier transform of functions which are compactly supported. The constraint that the functions have compact support is a simplifying feature which is desirable in applications, but there is a trade-off in control of other relevant quantities-- such as the mass of the function. With applications in mind, we prove inequalities which quantify these types of trade-offs. / text