La thèse est consacrée aux estimations de multiplicité. Ce type de résultats est utilisé en théorie de la transcendance. A partir des travaux de A. B. Shidlovskii, W.D.Brownawell et D.W.Masser il sont régulièrement utilisés dans les preuves de transcendance et surtout d'indépendance algébrique. Par exemple, la démonstration du lemme de multiplicité est un élément très important de la preuve par Yu. Nesterenko du résultat sur l'indépendance algébrique des valeurs des fonctions de Ramanujan. Un autre résultat de ce type est une preuve par K.Nishioka d'une conjecture de K.Mahler. Ce lemme de multiplicité a permis de démontrer beaucoup de résultats concernant la transcendance des séries liées aux suites récurrentes et des suites engendrées par des automates finis. Le but de ce mémoire est l'étude approfondie, dans un cadre général, des lemmes de multiplicité conduisant à des améliorations de résultats d'indépendance algébrique connus. Le théorème principal de ce travail réduit la preuve des estimations de multiplicité à l'étude des idéaux stables sous une transformation algébrique. En particulier, ce théorème permet d'améliorer un peu le résultat de Yu.Nesterenko concernant les solutions de système d'équations différentielles. Dans le même temps ce théorème donne, sous une condition concernant des variétés stables, l'estimation avec l'exposant le meilleur possible dans le cas de solutions d'équations fonctionnelles. Ce dernier résultat conduit à l'étude des variétés irréductibles stables sous une transformation rationnelle, ceci semble d'être un sujet intéressant en soi.

Gustav Mahler’s Lieder eines fahrenden Gesellen (first published 1887) feature as their only character a miserable wayfarer who laments his unrequited love for someone and who, in spite of all his beautiful pastoral surroundings, cannot help but feel deep unhappiness. Using Lacan’s three orders (Imaginary, Symbolic and Real) and further developments of his theory by Slavoj Žižek in The Sublime Object of Ideology, I argue that the eyes of the wayfarer’s beloved are the Lacanian Real that disrupts his symbolic network and thus are the origin of his traumatic existence. His misery becomes an immanent part of his identity and he can therefore only exist through this feeling. Furthermore I suggest that, although he laments the situation, he subconsciously desires the unhappy love affair as a way of guaranteeing his own existence as a wayfarer, in accordance with Freud’s concept of Repetition compulsion.

<p>This dissertation explores the meaning of art and religion in fin-de-siècle Vienna through the symphonies of the composer Gustav Mahler (1860-1911) and the philosophical and dramatic works of the poet Siegfried Lipiner (1856-1911). Using as a framework aesthetic discourses concerning the ability of music to be "read" as a narrative text, this study highlights the significant role of both poet and composer in the cultural and intellectual world of Vienna at the end of the nineteenth century. In this study, I compare and contrast Lipiner's vision of religious renewal with the redemptive narratives in the programs of Mahler's first four symphonies, which were composed during a period when the poet and composer shared a close friendship and intellectual exchange. Furthermore, I also discuss Mahler and Lipiner's works in relation to the writings of the Polish Romantic poet, Adam Mickiewicz (1798-1835), the philosopher Friedrich Nietzsche (1844-1900), and the composer and cultural critic, Richard Wagner (1813-1883), demonstrating how the images of the heroic martyr, the Übermensch and the Volk, play a role in the re-conception of man's relationship to the divine, which is central to Mahler and Lipiner's idea of redemption. However, I also claim that the political and cultural climate of Vienna around 1900 played an important role in their interpretation of these ideas. Despite their public conversion and cultural assimilation, Mahler and Lipiner's Jewish heritage distinctly shaped their interest in artistic-religious redemption both to cope with their own personal feelings of alienation in the society in which they lived, and as a cure for the existential malaise of their time. This study demonstrates not only the significant impact of Lipiner's aesthetic-religious philosophy on Mahler's music, but also portrays their vision of redemption as an re-envisioning of man's relationship to God, which stands in contrast to the modern trend of secularism, and reflects a little-explored dimension of aesthetic and religious culture in fin-de-siècle Vienna.</p> / Dissertation

Gustav Mahler (1860-1911), was one of the great composers of the late-Romantic era. He composed forty-five Lieder. These Lieder, as influences by Mahler¡¦s symphonic work, show a broader scope, in terms of the sound, the length and the tension, as compared to Lieder by previous composers. Impacted by Romanism and Nationalism, Mahler composed twenty-three Wunderhorn-Lieder, which based on Des Knaben Wunderhorn by German poets Achim von Arnim (1781¡V1831) and Clemens Brentano (1976¡V1842). The Wunderhorn anthology has more than seven hundreds poems, which is a significant piece of German literature work for folk songs. Four Wunderhorn-Lieder are discussed in this paper: ¡§Ich ging mit Lust durch einen grünen Wald,¡§Scheiden und Meiden¡¨, ¡§Wer hat die Liedlein erdacht¡H¡¨, and¡§ Wo die schönen Trompeten blasen¡¨. The main theme of these four Lieder is love, and each of them represents a different type of love experience. The study mainly contains four parts: the biographical information about Gustav Mahler, the Lieder of Gustav Mahler, a brief introduction of poets Arnim and Brentano, and a performance analysis of the four Wunderhorn-Lieder. Through analyzing these four Lieder, we can gain insight into how poetry was played up and extended by Mahler using music, and help the vocalists better express the spirit and the music syntax of Mahler when interpreting his Lieder.

In this thesis we study Mahler's conjecture in convex geometry, give a short summary about its history, gather and explain different approaches that have been used to attack the conjecture, deduce formulas to calculate the Mahler volume and perform numerical analysis on it. The conjecture states that the Mahler volume of any symmetric convex body, i.e. the product of the volume of the symmetric convex body and the volume of its dual body, is minimized by the (hyper-)cube. The conjecture was stated and solved in 1938 for the 2-dimensional case by Kurt Mahler. While the maximizer for this problem is known (it is the ball), the conjecture about the minimizer is still open for all dimensions greater than 2. A lot of effort has benn made to solve this conjecture, and many different ways to attack the conjecture, from simple geometric attempts to ones using sophisticated results from functional analysis, have all been tried unsuccesfully. We will present and discuss the most important approaches. Given the support function of the body, we will then introduce several formulas for the volume of the dual and the original body and hence for the Mahler volume. These formulas are tested for their effectiveness and used to perform numerical work on the conjecture. We examine the conjectured minimizers of the Mahler volume by approximating them in different ways. First the spherical harmonic expansion of their support functions is calculated and then the bodies are analyzed with respect to the length of that expansion. Afterwards the cube is further examined by approximating its principal radii of curvature functions, which involve Dirac delta functions.

By the 1960s, the music of Austrian composer Gustav Mahler had become an exceptionally--and enduringly--popular part of American concert life. But for much of the twentieth century, the place of Mahler's music in America's orchestral canon was passionately debated and not nearly so secure. This dissertation proposes that the growth of transatlantic modernism--in some ways a reaction to Mahler's Austro-German tradition--went hand in hand with the developing appreciation for Mahler's music in the United States between 1920 and 1960. This study focuses on the relationship between this new appreciation for Mahler in America and a network of four influential figures in transatlantic modernism: Nadia Boulanger, the French musician who taught a whole generation of prominent American modernist composers; Aaron Copland, who would become one of the most significant and outspoken figures in American modernism; Serge Koussevitzky, the celebrated conductor of the Boston Symphony Orchestra; and Leonard Bernstein, the composer and conductor most recognized for having popularized Mahler’s music. These figures shared their ideas on Mahler but also developed their own distinctive ones. This dissertation argues that between 1920, when Boulanger attended and wrote about a Mahler festival in Amsterdam, possibly her introduction to Mahler’s music, and 1960, when Bernstein led the New York Philharmonic in a celebration of the Mahler centenary, these four musicians played a significant role in shaping ideas about Mahler in America, and that they did so by placing Mahler in the specific contexts of their priorities as modernists. Methodologically, this study uses archival evidence to unite two strands of recent, significant musicological inquiry: the transnational history of American musical culture, and the transmission, reception, and circulation of music in interpersonal networks. / Music

In this thesis, we introduce and study several norms constructed to satisfy an extremal property with respect to the Mahler measure. These norms naturally generalize the metric Mahler measure introduced by Dubickas and Smyth. We show that bounding these norms on a certain subspace implies Lehmer's conjecture and in at least one case that the converse is true as well. We evaluate these norms on a class of algebraic numbers that include Pisot and Salem numbers, and for surds. We prove that the infimum in the construction is achieved in a certain finite dimensional space for all algebraic numbers in one case, and for surds in general, a finiteness result analogous to that of Samuels and Jankauskas for the t-metric Mahler measures. Next, we generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a Q-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over Q retain their linear independence over R. / text

Musical analysis has traditionally been located within the context of musicology. It is therefore an activity usually considered the purview of music scholars rather than practical musicians. The musical analyses produced by music scholars therefore provide us with intellectual understandings of musical works, rather than insights into the experience of listening to or playing music. In this thesis, I will propose that those agents involved in practical music-making can produce insights into musical works that are as valid as the work of traditional music scholarship. I will attempt to re-conceptualize the position of the ‘knower’ or ‘experiencer’ - the performer - of music as one with primary access to knowledge of a musical work, and therefore ideally suited to offer analyses of these works. The establishment of the performer as a bearer of central analytical knowledge functions in direct opposition to the traditional distinction between ‘theory’ and ‘practice’. My thesis will trace the Platonic origins of the philosophical separation of practice and research, and as an alternative to the traditional separation of practice and research, I shall explore the concept of Practice-Based Research (PBR). My exploration of PBR will be informed by phenomenological approaches to music scholarship. As a field of enquiry which concerns itself with experience, the phenomenology of music suggests that the mind and body of the practitioner are important sources of musical insight. To address this issue, Bourdieu’s notion of habitus will be explored. The habitus will be shown to contain a vast network of socio-cultural codes informing the practitioner’s relationship with the musical work. A central aim of this thesis is to explore the possibilities of using practice-based research as the foundation for the study and analysis of a composition, in order to allow for a deeper understanding of the work by means of the generation and harnessing of practical knowledge. Thus, the theoretical outline of PBR provided in this thesis will be applied to a piece of practical performance-based analysis. As such, an analysis of Mahler’s Quartetsatz will be used as the basis on which to draw knowledge in this project.

Cette thèse se situe dans le domaine de la théorie des nombres. Elle traite de la transcendance et de l'indépendance algébrique de valeurs de fonctions mahlériennes définies sur des corps de fonctions de caractéristique p>0. La problématique de cette thèse est l'établissement de l'équivalence entre l'indépendance algébrique de valeurs de fonctions mahlériennes aux points algébriques et celle des fonctions elles-mêmes. L'une de nos motivations est l'observation fructueuse de L. Denis selon laquelle il est possible en caractéristique non nulle de déformer des nombres remarquables (périodes de modules de Drinfeld) comme valeurs de fonctions mahlériennes. Nous démontrons notamment que toute relation algébrique homogène entre valeurs, en un point algébrique non nul régulier, de solutions d'un système mahlérien engendrant une extension régulière, provient de la spécialisation d'une relation algébrique homogène entre les fonctions elles-mêmes. Il s'agit de l'analogue de travaux de P. Philippon et de B. Adamczewski et C. Faverjon et d'un raffinement d'un théorème fondamental de Ku. Nishioka, dans le cas où K est un corps de nombres. Ainsi, l'étude de l'indépendance algébrique des valeurs de fonctions mahlériennes se ramène à celle des fonctions elles-mêmes. Cependant, contrairement à la caractéristique nulle, une fonction mahlérienne algébrique n'est pas nécessairement rationnelle et la transcendance de fonctions mahlériennes dans ce contexte demeure encore mystérieuse. Néanmoins, nous établissons que cette dichotomie reste valide pour les fonctions d-mahlériennes, où p ne divise pas d. Par ailleurs, nous démontrons un théorème de type Kolchin qui fournit une condition suffisante à l'indépendance algébrique de fonctions mahlériennes d'ordre 1 inhomogène ainsi qu'une caractérisation de la transcendance de telles fonctions. Enfin, au-delà de ces résultats qualitatifs, nous nous intéressons aux mesures d’indépendance algébrique entre valeurs de fonctions mahlériennes en caractéristique non nulle et proposons une approche, inspirée de travaux récents de E. Zorin en caractéristique nulle, qui permettrait d’obtenir de tels résultats quantitatifs / This thesis is part of Number Theory. It deals with transcendence and algebraic independence of values of Mahler functions over function fields of characteristic p>0. The starting point of this thesis is to prove the equivalence between algebraic independence of values of Mahler functions at algebraic points and that of the functions themselves. One of our main motivations is the fruitful observation due to L. Denis that it is possible to reach special numbers (periods of Drinfeld modules) as values of Mahler functions in positive characteristic. We show that every homogeneous algebraic relation between values of solutions of Mahler systems, which generate regular extensions, at nonzero algebraic regular numbers, arises as specialization of an homogeneous algebraic relation between the functions themselves. This is the analogue of the work of P. Philippon and B. Adamczewski and C. Faverjon, and a refinement of a fundamental theorem from Ku. Nishioka, when K is a number field. Thus, the study of algebraic independence between values of Mahler functions turns into that between the functions themselves. But algebraic Mahler functions over function fields of positive characteristic are not necessarily rational, contrary to the number fields case. Transcendence of Mahler functions in this framework still remains mysterious. Nevertheless, we state that this dichotomy is still valid for d-Mahler functions, when p does not divide d. Moreover, we prove a Kolchin theorem that provides a sufficient condition for algebraic independence of inhomogeneous Mahler functions of order 1, along with a characterization of the transcendence of such functions. Finally, we are interested in algebraic independence measures of values of Mahler functions in positive characteristic. We suggest an approach, based on a recent work of E. Zorin in characteristic zero, which would give such qualitative results in our context

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