We prove in this thesis three main results, involving the distribution of values of $L'/L(\sigma,\chi_D)$,$D$ being a fundamental discriminant, and $\chi_D$ the real character attached to it. We prove two Omega theorems for $L'/L(1,\chi_D)$, compute the moments of $L'/L(1,\chi_D)$, and construct under GRH, for each $\sigma>1/2$,a density function ${\cal Q}_\sigma$ such that
\[\#\{D ~~\text{fundamental discriminants, such that}~~ |D|\leq Y,~~ \text{and}~~ \alpha \leq L'/L(\sigma,\chi_D)\leq \beta \}
\]\[ \sim \frac{6}{\pi^2\sqrt{2\pi}} Y \int_\alpha^\beta {\cal Q}_\sigma(x)dx .
\]
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OTU.1807/35913 |
| Date | 09 August 2013 |
| Creators | Mourtada, Mariam Mohamad |
| Contributors | Murty, V. Kumar |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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