Welcome to our book review site go-pdf.online!
You may have to Search all our reviewed books and magazines, click the sign up button below to create a free account.
Level One Algebraic Cusp Forms of Classical Groups of Small Rank
The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.
Equivalent Definitions of Arthur Packets for Real Classical Groups
View the abstract.
On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III
Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.
Harmonic Analysis, the Trace Formula, and Shimura Varieties
Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
On Some Aspects of Oscillation Theory and Geometry
The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.
On the Steady Motion of a Coupled System Solid-Liquid
We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B,L}, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.
On the Regularity of the Composition of Diffeomorphisms
For M a closed manifold or the Euclidean space Rn we present a detailed proof of regularity properties of the composition of Hs-regular diffeomorphisms of M for s > 12dimM+1.
Spectral Decomposition of a Covering of $GL(r)$: the Borel case
Let $F$ be a number field and ${\bf A}$ the ring of adeles over $F$. Suppose $\overline{G({\bf A})}$ is a metaplectic cover of $G({\bf A})=GL(r, {\bf A})$ which is given by the $n$-th Hilbert symbol on ${\bf A}$
Geometric Aspects of the Trace Formula
The second of three volumes devoted to the study of the trace formula, these proceedings focus on automorphic representations of higher rank groups. Based on research presented at the 2016 Simons Symposium on Geometric Aspects of the Trace Formula that took place in Schloss Elmau, Germany, the volume contains both original research articles and articles that synthesize current knowledge and future directions in the field. The articles discuss topics such as the classification problem of representations of reductive groups, the structure of Langlands and Arthur packets, interactions with geometric representation theory, and conjectures on the global automorphic spectrum. Suitable for both graduate students and researchers, this volume presents the latest research in the field. Readers of the first volume Families of Automorphic Forms and the Trace Formula will find this a natural continuation of the study of the trace formula.
