Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 57-59). Also available in electronic version.

In this thesis we study Kudla’s special cycles of codimension 𝑟 on a unitary Shimura variety Sh(U(𝑚 − 1,1)) together with an embedding of a Shimura subvariety Sh(U(𝑚 − 1,1)). We prove that when 𝑟 = 𝑛 − 𝑚, for certain cuspidal automorphic representations 𝜋 of the quasi-split unitary group U(𝑟,𝑟) and certain cusp forms ⨍ ∈ 𝜋, the geometric volume of the pullbackof the arithmetic theta lift of ⨍ equals the special value of the standard 𝐿-function of 𝜋 at 𝑠 = (𝑚 − 𝑟 + 1)/2. As ingredients of the proof, we also give an exposition of Kudla’s geometric Siegel-Weil formula and Yuan-Zhang-Zhang’s pullback formula in the setting of unitary Shimura varieties, as well as Qin’s integral representation result for 𝐿-functions of quasi-split unitary groups.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematical Sciences." Includes bibliographical references (p. 74).

Thesis (Doctoral)--Universität Bonn, 1991. / Includes bibliographical references.

No description available.

Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.

In this thesis, we prove that local genericity implies globally genericity for the quasi-split unitary group U3 for a quadratic extension of number fields E/F. We follow [Fli1992] and [GJR2001] closely, using the relative trace formula approach. Our main result is the existence of smooth transfer for the relative trace formulae in [GJR2001], which is circumvented there. The basic idea is to compute the Mellin transform of Shalika germ functions and show that they are equal in the unitary case and the general linear case.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 61-62). Also available in electronic version. Access restricted to campus users.

In this work, we explore the NN → πNN reaction within a relativistic model, consistent with two- and three-body unitarity, for the NN and πNN coupled systems. The model is based on effective hadronic interactions. After describing the theoretical input, we compare the predicted NN phase parameters with the phase shift analysis. Our predictions for the NN → πNN spin observables are compared with the available data and with predictions from other models. A clear model dependence is observed. We also examine systematically the dependence of these spin observables on various components of the dynamical input. We identify and isolate some problems related to the present approach and we point out possible directions for future research. / Ph. D.

In this thesis, we prove a Kudla-Rapoport conjecture for 𝓨-cycles on exotic smooth unitary Rapoport-Zink spaces of odd arithmetic dimension, i.e. the arithmetic intersection numbers for 𝓨-cycles equals the derivatives of local representation density. We also compare 𝓩-cycles and 𝓨-cycles on these RZ spaces. The method is to relate both geometric and analytic sides to the even dimensional case and reduce the conjecture to the results in \cite{LL22}.