Families of Automorphic Forms and the Trace Formula

Description

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory.  Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals. Front Matter....Pages i-xii Germ Expansions for Real Groups....Pages 1-91 Slopes of Modular Forms....Pages 93-109 Transfer Principles for Bounds of Motivic Exponential Functions....Pages 111-127 Growth of Hecke Fields Along a p-Adic Analytic Family of Modular Forms....Pages 129-173 The Trace Formula and Prehomogeneous Vector Spaces....Pages 175-215 The Local Langlands Conjectures for Non-quasi-split Groups....Pages 217-257 Asymptotics and Local Constancy of Characters of p-adic Groups....Pages 259-295 Endoscopy and Cohomology of a Quasi-Split U(4)....Pages 297-325 Distribution of Hecke Eigenvalues for GL(n)....Pages 327-350 Zeta Functions for the Adjoint Action of GL(n) and Density of Residues of Dedekind Zeta Functions....Pages 351-433 Some Results in the Theory of Low-Lying Zeros of Families of L-Functions....Pages 435-476 Asymptotics of Automorphic Spectra and the Trace Formula....Pages 477-529 Families of L-Functions and Their Symmetry....Pages 531-578