Consider either (i) f = f1 ⊠ f2 for two Maass cusp forms for SLm(ℤ) and SLm′(ℤ), respectively, with 2 ≤ m ≤ m′, or (ii) f= f1 ⊠ f2 ⊠ f3 for three weight 2k holomorphic cusp forms for SL2(ℤ). Let λf(n) be the normalized coefficients of the associated L-function L(s, f), which is either (i) the Rankin-Selberg L-function L(s, f1 ×f2), or (ii) the Rankin triple product L-function L(s, f1 ×f2 ×f3). First, we derive a Voronoi-type summation formula for λf (n) involving the Meijer G-function. As an application we obtain the asymptotics for the smoothly weighted average of λf (n) against e(αnβ), i.e. the asymptotics for the associated resonance sums. Let ℓ be the degree of L(s, f). When β = 1/ℓ and α is close or equal to ±ℓq 1/ℓ for a positive integer q, the average has a main term of size |λf (q)|X 1/2ℓ+1/2 . Otherwise, when α is fixed and 0 < β < 1/ℓ it is shown that this average decays rapidly. Similar results have been established for individual SLm(ℤ) automorphic cusp forms and are due to the oscillatory nature of the coefficients λf (n).

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.

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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 1997. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 420-429).

Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 1997. / Includes bibliographical references (leaves 420-429).

Thesis (Ph.D.) - University of St Andrews, March 2010. / Electronic version restricted until 1st March 2015.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22231号 / 理博第4545号 / 新制||理||1653(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 池田 保, 教授 雪江 明彦, 教授 並河 良典 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In this thesis, we define differential operators for Hermitian Jacobi forms and Hermitian modular forms over the Gaussian number field Q(i). In particular, we construct Rankin-Cohen brackets for such spaces of Hermitian Jacobi forms and Hermitian modular forms. As an application, we extend Rankin's method to the case of Hermitian Jacobi forms. Finally we compute Fourier series coefficients of Hermitian modular forms, which allow us to give an example of the first Rankin-Cohen bracket of two Hermitian modular forms. In the appendix, we provide tables of Fourier series coefficients of Hermitian modular forms and also the computer source code that we used to compute such Fourier coefficients.

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<p><strong>Objective: </strong>Despite the known benefits of prenatal care, not all women access it equally. Evidence suggests women in Nunavut utilize prenatal care less than in any other jurisdiction in Canada and there is an absence of literature that explains why. This study seeks to improve our understanding of the factors influencing utilization of prenatal care for women in Nunavut by exploring the barriers, facilitators and motivators to utilization.</p> <p><strong>Methods: </strong>A qualitative, descriptive approach was used. Community collaboration informed the research process. Data were analyzed from 21 semi-structured interviews conducted with pregnant and postpartum women and maternity care providers in two Nunavut communities. Using a socioecological model of health services utilization and inductive content analysis, transcribed interviews were analysed to determine the factors that influence prenatal care utilization.</p> <p><strong>Findings: </strong>Utilization of prenatal care was influenced by personal, situational and system-related barriers, facilitators and motivators. Personal and situational barriers, facilitators and motivators to care were similar among women from both communities. System-related barriers and facilitators, related to the model of prenatal care and its delivery, differed between the two communities with barriers including language, appointment scheduling and waiting times.</p> <p><strong>Conclusion: </strong>System-related barriers reduced access to prenatal care for women in one Nunavut community. Access may be improved in communities with low utilization by revising the current model of prenatal care to reflect care delivered in communities where care providers have dedicated prenatal care roles.</p> / Master of Science (MSc)