<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Quaternionic Drinfeld modular forms"^^ . "Drinfeld modular forms were introduced by D. Goss in 1980 for congruence subgroups of ${\\rm GL}_2(\\mathbb{F}_q[T])$. They are a counterpart of classical modular forms in the function field world. In this thesis I study Drinfeld modular forms for inner forms of ${\\rm GL}_2$ that correspond to unit groups $\\Lambda^\\star$ of quaternion division algebras over $\\mathbb{F}_q(T)$ split at the place $\\infty = 1/T$. I show, following work of Teitelbaum for ${\\rm GL}_2(\\mathbb{F}_q[T])$, that these forms have a combinatorial interpretation as certain maps from the edges of the Bruhat-Tits tree $\\mathcal{T}$ associated to ${\\rm PGL}_2(K_\\infty)$. Here $K_\\infty$ denotes the completion of $K$ at $\\infty$. A major focus of this thesis is on computational aspects: I present an algorithm for computing a fundamental domain for the action of $\\Lambda^\\star$ on $\\mathcal{T}$ with an edge pairing, and describe how to obtain a basis of the space of these forms out of this fundamental domain. On this basis one can compute the Hecke action.\r\n"^^ . "2012-10-24" . . . . . . . "Ralf"^^ . "Butenuth"^^ . "Ralf Butenuth"^^ . . . . . . "Quaternionic Drinfeld modular forms (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Quaternionic Drinfeld modular forms (PDF)"^^ . . . "Dissertation_Ralf-Butenuth.pdf"^^ . . . "Quaternionic Drinfeld modular forms (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Quaternionic Drinfeld modular forms (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Quaternionic Drinfeld modular forms (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Quaternionic Drinfeld modular forms (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #13885 \n\nQuaternionic Drinfeld modular forms\n\n" . "text/html" . . . "510 Mathematik"@de . "510 Mathematics"@en . .