Non-coding RNAs (ncRNAs) have emerged as highly diverse and powerful key players in the cell, the range of capabilities spanning from catalyzing essential processes in all living organisms, e.g. protein synthesis, to being highly specific regulators of gene expression. To fully understand the functional significance of ncRNAs, it is of critical importance to identify and characterize the repertoire of ncRNAs in the cell. Practically every genome-wide screen to identify ncRNAs has revealed large numbers of expressed ncRNAs and often identified species-specific ncRNA families of unknown function. Recent years' advancement in high-throughput sequencing techniques necessitates efficient and reliable methods for computational identification and annotation of genes. A major aim in the work underlying this thesis has been to develop and use computational tools for the identification and characterization of ncRNA genes. We used computational approaches in combination with experimental methods to study the ncRNA repertoire of the model organism Dictyostelium discoideum. We report ncRNA genes belonging to well-characterized gene families as well as previously unknown and potentially species-specific ncRNA families. The complicated task of de novo ncRNA gene prediction was successfully addressed by developing a method for nucleotide composition-based gene prediction using maximal-scoring partial sums and considering overlapping dinucleotides. We also report a substantial heterogeneity among human spliceosomal snRNAs. Northern blot analysis and cDNA cloning, as well as bioinformatical analysis of publicly available microarray data, revealed a large number of expressed snRNAs. In particular, U1 snRNA variants with several nucleotide substitutions that could potentially have dramatic effects on splice site recognition were identified. In conclusion, we have by using computational approaches combined with experimental analysis identified a rich and diverse ncRNA repertoire in the eukaryotes D. discoideum and Homo sapiens. The surprising diversity among the snRNAs in H. sapiens suggests a functional involvement in recognition of non-canonical introns and regulation of messenger RNA splicing.

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Nous traitons trois problèmes liés à la fonction zêta de Riemann : 1) L'établissement de conditions pour déterminer l'alignement et la simplicité de la quasi-totalité des zéros d'une fonction de la forme f(s)=h(s)±h(2c-s), où h(s) est une fonction méromorphe et c un nombre réel. Cela passe par la généralisation du théorème d'Hermite-Biehler sur la stabilité des fonctions entières. Comme application, nous avons obtenu des résultats sur la répartition des zéros des translatées de la fonction zêta de Riemann et de fonctions L, ainsi que sur certaines intégrales de séries d'Eisenstein. 2) L'étude de la répartition des zéros des sommes partielles de la fonction zêta, et des ses approximations issues de la formule d'Euler-Maclaurin. 3) L'étude du prolongement méromorphe et de la frontière naturelle pour une classe de produits eulériens, qui inclut une série de Dirichlet utilisée dans l'étude de la répartition des valeurs de l'indicatrice d'Euler. / We deal with three problems related to the Riemann zeta function: 1) The establishment of conditions to determine the alignment and simplicity of most of the zeros of a function of the form f(s)=h(s)±h(2c-s), where h(s) is a meromorphic function and c a real number. To this end, we generalise the Hermite-Biehler theorem concerning the stability of entire functions. As an application, we obtain some results about the distribution of zeros of translations of the Riemann Zeta Function and L functions, and about certain integrals of Eisenstein series. 2) The study of the distribution of the zeros of the partial sums of the zeta function, and of some approximations issued from the Euler-Maclaurin formula. 3) The study of the meromorphic continuation and the natural boundary of a class of Euler products, which includes a Dirichlet series used in the study of the distribution of values of the Euler totient.

Cette thèse se compose de deux projets. Le premier concerne la structure des fonctions multiplicatives dont les moyennes sont petites. En particulier, dans ce projet, nous établissons le comportement moyen des valeurs \(f(p)\) de \(f\) aux nombres premiers pour des fonctions \(f\) multiplicatives appropriées lorsque leurs sommes partielles \(\sum_{n\leqslant x}f(n)\) sont plus petites que leur borne supérieure triviale par un facteur d′une puissance de \(\log x\). Ce résultat poursuit un travail antérieur de Koukoulopoulos et Soundararajan et il est construit sur des idées provenant du traitement plus soigné de Koukoulopoulos sur le cas special des fonctions multiplicatives bornées. Le deuxième projet de la thèse est inspiré par un analogue d’une estimation que Linnik a déduit dans sa tentative de prouver son célèbre théorème concernant la taille du plus petit nombre premier d’une progression arithmétique. Cette estimation fournit une formule asymptotique fortement uniforme pour les sommes de la fonction de von Mangoldt \(\Lambda\) sur les progressions arithmétiques. Dans la littérature, ses preuves existantes utilisent des informations non triviales sur les zéros des fonctions \(L\) de Dirichlet \(L(\cdot,\chi)\) et le but du deuxième projet est de présenter une approche différente, plus élémentaire qui récupère cette estimation en évitant la “langue” de ces zéros. Pour le développement de cette méthode alternative, nous utilisons des idées qui apparaissent dans le grand crible prétentieux (pretentious large sieve) de Granville, Harper et Soundararajan. De plus, comme dans le cas du premier projet, nous empruntons également des idées du travail de Koukoulopoulos sur la structure des fonctions multiplicatives bornées à petites moyennes. / This thesis consists of two projects. The first one is concerned with the structure of multiplicative functions whose averages are small. In particular, in this project, we establish the average behaviour of the prime values \(f(p)\) for suitable multiplicative functions \(f\) when their partial sums \(\sum_{n\leqslant x}f(n)\) admit logarithmic cancellations over their trivial upper bound. This result extends previous related work of Koukoulopoulos and Soundararajan and it is built upon ideas coming from the more careful treatment of Koukoulopoulos on the special case of bounded multiplicative functions. The second project of the dissertation is inspired by an analogue of an estimate that Linnik deduced in his attempt to prove his celebrated theorem regarding the size of the smallest prime number of an arithmetic progression. This estimate provides a strongly uniform asymptotic formula for the sums of the von Mangoldt function \(\Lambda\) on arithmetic progressions. In the literature, its existing proofs involve non-trivial information about the zeroes of Dirichlet \(L\)-functions \(L(\cdot,\chi)\) and the purpose of the second project is to present a different, more elementary approach which recovers this estimate by avoiding the “language” of those zeroes. For the development of this alternative method, we make use of ideas that appear in the pretentious large sieve of Granville, Harper and Soundararajan. Moreover, as in the case of the first project, we also borrow insights from the work of Koukoulopoulos on the structure of bounded multiplicative functions with small averages.