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.
Germ expansions for real groups (J. Arthur).- Slopes of modular forms (K. Buzzard, T. Gee).- Transfer principles for bounds of motivic exponential functions (R. Cluckers, J. Gordon I. Halupczok).- Growth of Hecke fields along a p-adic analytic family of modular forms (H. Hida).- The trace formula and prehomogeneous vector spaces (W. Hoffmann).- The local Langlands conjectures for non-quasi-split groups (T. Kaletha).- Asymptotics and local constancy of characters of p-adic groups (J.-L. Kim, S.-W. Shin, N. Templier).- Endoscopy and cohomology of a quasi-split U(4) (S. Marshall).- Distribution of Hecke Eigenvalues for GL(n) (J. Matz).- Zeta functions for the adjoint action of GL(n) and density of residues of Dedekind zeta functions (J. Matz).- Some results in the theory of low-lying zeros of families of L-functions (B. Mackall, S. Miller, C. Rapti, C. Turnage-Butterbaugh, K. Winsor).- Asymptotics of automorphic spectra and the trace formula (W. Müller).- Families of L-functions and
their symmetry (P. Sarnak, S.-W. Shin, N. Templier).
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