Memoirs of the American Mathematical Society 2009; 172 pp; softcover Volume: 204 ISBN10: 0821848224 ISBN13: 9780821848227 List Price: US$77 Individual Members: US$46.20 Institutional Members: US$61.60 Order Code: MEMO/204/957
 Let \(F\) be a number field or a \(p\)adic field. The author introduces in Chapter 2 of this work two reductive rank one \(F\)groups, \(\mathbf{H_1}\), \(\mathbf{H_2}\), which are twisted endoscopic groups of \(\mathrm{GSp}(2)\) with respect to a fixed quadratic character \(\varepsilon\) of the idèle class group of \(F\) if \(F\) is global, \(F^\times\) if \(F\) is local. When \(F\) is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of \(\mathbf{H_1}\), \(\mathbf{H_2}\) to those of \(\mathrm{GSp}(2)\). In Chapter 4, the author establishes this lifting in terms of the Satake parameters which parameterize the automorphic representations. By means of this lifting he provides a classification of the discrete spectrum automorphic representations of \(\mathrm{GSp}(2)\) which are invariant under tensor product with \(\varepsilon\). Table of Contents  Introduction
 \(\varepsilon\)endoscopy for \(\mathrm{GSp}(2)\)
 The trace formula
 Global lifting
 The local picture
 Appendix A. Summary of global lifting
 Appendix B. Fundamental lemma
 Bibliography
 List of symbols
 Index
