Families of Automorphic Forms and the Trace Formula

1. Front Matter

   Pages i-xii

   PDF

2. Germ Expansions for Real Groups

   • James Arthur

   Pages 1-91

3. Slopes of Modular Forms

   • Kevin Buzzard, Toby Gee

   Pages 93-109

4. Transfer Principles for Bounds of Motivic Exponential Functions

   • Raf Cluckers, Julia Gordon, Immanuel Halupczok

   Pages 111-127

5. Growth of Hecke Fields Along a p-Adic Analytic Family of Modular Forms

   • Haruzo Hida

   Pages 129-173

6. The Trace Formula and Prehomogeneous Vector Spaces

   • Werner Hoffmann

   Pages 175-215

7. The Local Langlands Conjectures for Non-quasi-split Groups

   • Tasho Kaletha

   Pages 217-257

8. Asymptotics and Local Constancy of Characters of p-adic Groups

   • Ju-Lee Kim, Sug Woo Shin, Nicolas Templier

   Pages 259-295

9. Endoscopy and Cohomology of a Quasi-Split U(4)

   • Simon Marshall

   Pages 297-325

10. Distribution of Hecke Eigenvalues for GL(n)

    • Jasmin Matz

    Pages 327-350

11. Zeta Functions for the Adjoint Action of GL(n) and Density of Residues of Dedekind Zeta Functions

    • Jasmin Matz

    Pages 351-433

12. Some Results in the Theory of Low-Lying Zeros of Families of L-Functions

    • Blake Mackall, Steven J. Miller, Christina Rapti, Caroline Turnage-Butterbaugh, Karl Winsor

    Pages 435-476

13. Asymptotics of Automorphic Spectra and the Trace Formula

    • Werner Müller

    Pages 477-529

14. Families of L-Functions and Their Symmetry

    • Peter Sarnak, Sug Woo Shin, Nicolas Templier

    Pages 531-578

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.

• L-functions and symmetry
• automorphic forms
• trace formula
• families of automorphic representations of higher rank groups
• spectra of locally symmetric spaces
• p-adic families
• harmonic analysis and representation theory
• counting cohomological forms
• p-adic trace formulas
• Hecke fields
• slopes of modular forms
• orbital integrals

• Mathematical Institute, University of Bonn, Bonn, Germany

  Werner Müller

• Department of Mathematics, University of California, Berkeley, Berkeley, USA

  Sug Woo Shin

• Department of Mathematics, Cornell University, Ithaca, USA

  Nicolas Templier

Werner Müller is Professor Emeritus at the Mathematical Institute of the University of Bonn. He is the author of over fifty publications, including articles in Inventiones Mathematicae, Geometric and Functional Analysis, and Communications in Mathematical Physics. His research interests include geometric analysis, scattering theory, analytic theory of automorphic forms, and harmonic analysis on locally symmetric spaces.


Sug Woo Shin is Associate Professor of Mathematics at the University of California at Berkeley. His research is centered on number theory, Shimura varieties, Langlands functoriality, trace formula, and automorphic forms. His work has appeared in many journals, including Inventiones Mathematicae, Mathematische Annalen, and the Israel Journal of Mathematics.


Nicolas Templier is Associate Professor of Mathematics at Cornell University. His work focuses on number theory, automorphic forms, arithmetic geometry, ergodic theory, and mathematical physics. His list of publications include articles in Inventiones Mathematicae, the Ramanujan Journal, and the Israel Journal of Mathematics.

Policies and ethics