In this paper we deduce a prime number theorem for the L-function L(s; AIE=Q() AIF=Q(0)) where and 0 are automorphic cuspidal representations of GLn=E and GLm=F, respectively, with E and F solvable algebraic number elds with a Galois invariance assumption on the representations. Here AIF=Q denotes the automorphic induction functor. We then use the proof of the prime number theorem to compute the n-level correlation function of a product of L-functions dened over cyclic algebraic number elds of prime degree.

La présente thèse s'inscrit dans le cadre de travaux sur la représentation de Weil. Elle consiste en trois parties. Aux chapitres 2 et 3, on généralise la correspondance de Howe aux groupes de similitudes sur un corps local non archimédien de caractéristique résiduelle impaire. Aux chapitres 4 et 5, on répond dans beaucoup de cas à une question, soulevée par V. Drinfeld, sur la représentation de Weil de GSp8(F) de restreinte à un groupe GL2(A), où A est une algègre étale sur un corps local ou fini F. D'autre part, au chapitre 5, on montre que sur un corps fini, les représentations de Weil sont compatibles au changement de base au sens de Shintani-lift. / This present thesis is working on the Weil representation. It consists of three parts. In chapter 2 and chapter 3, we generalize the Howe correspondance for the similitudes groupes over the non archimedien field with odd residual characteristic. In chapter 4 and chapter 5, we answer one question, raised by V. Drinfeld, about the restriction of the Weil representation of the group GSp8(F) to GL2(A) where A is an étale algebra over a non archimedien field or a finite field F. On the other hand, in the chapter 5, we prove that in finite field case, the Weil representations are invariant under the operator of base change in the sens of Shintani-lifting.

The thrust of this thesis is to describe base change BC_E/F at the level of chamber homology and K-theory for some p-adic groups, such as SL(2,F), GL(1,F) and GL(2,F). Here F is a non-archimedean local field and E is a Galois extension of F. We have had to master the representation theory of SL(2) and GL(2) including the Langlands parameters. The main result is an explicit computation of the effect of base change on the chamber homology groups, each of which is constructed from cycles. This will have an important connection with the Baum-Connes correspondence for such p-adic groups. This thesis involved the arithmetic of fields such as E and F, geometry of trees, the homology groups and the Weil group W_F.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22230号 / 理博第4544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

The ability to change one's beliefs in a rational manner is one of many facets of the abilities of an intelligent agent. Central to any investigation of belief change is the notion of an epistemic state. This dissertation is mainly concerned with three issues involving epistemic states: 1. How should an epistemic state be represented? 2. How does an agent use an epistemic state to perform belief change? 3. How does an agent arrive at a particular epistemic state? With regard to the first question, note that there are many different methods for constructing belief change operations. We argue that semantic constructions involving ordered pairs, each consisting of a set of beliefs and an ordering on the set of "possible worlds" (or equivalently, on the set of basic independent bits of information) are, in an important sense, more fundamental. Our answer to the second question provides indirect support for the use of semantic structures. We show how well-known belief change operations and related structures can be modelled semantically. Furthermore, we introduce new forms of belief change related operations and structures which are all defined, and motivated, in terms of such semantic representational formalisms. These include a framework for unifying belief revision and nonmonotonic reasoning, new versions of entrenchment orderings on beliefs, novel approaches to withdrawal operations, and an expanded view of iterated belief change. The third question is. one which has not received much attention in the belief change literature. We propose to extract extra-logical information from the formal representation of an agent's set of beliefs, which can then be used in the construction of epistemic state. his proposal is just a first approximation, although it seems to have the potential for developing into a full-fledged theory. / Computing / D.Phil.(Computer Science)

The ability to change one's beliefs in a rational manner is one of many facets of the abilities of an intelligent agent. Central to any investigation of belief change is the notion of an epistemic state. This dissertation is mainly concerned with three issues involving epistemic states: 1. How should an epistemic state be represented? 2. How does an agent use an epistemic state to perform belief change? 3. How does an agent arrive at a particular epistemic state? With regard to the first question, note that there are many different methods for constructing belief change operations. We argue that semantic constructions involving ordered pairs, each consisting of a set of beliefs and an ordering on the set of "possible worlds" (or equivalently, on the set of basic independent bits of information) are, in an important sense, more fundamental. Our answer to the second question provides indirect support for the use of semantic structures. We show how well-known belief change operations and related structures can be modelled semantically. Furthermore, we introduce new forms of belief change related operations and structures which are all defined, and motivated, in terms of such semantic representational formalisms. These include a framework for unifying belief revision and nonmonotonic reasoning, new versions of entrenchment orderings on beliefs, novel approaches to withdrawal operations, and an expanded view of iterated belief change. The third question is. one which has not received much attention in the belief change literature. We propose to extract extra-logical information from the formal representation of an agent's set of beliefs, which can then be used in the construction of epistemic state. his proposal is just a first approximation, although it seems to have the potential for developing into a full-fledged theory. / Computing / D.Phil.(Computer Science)