An Introduction to Automorphic Representations
with a view toward Trace Formulae

Jayce R. Getz and Heekyoung Hahn

Springer GTM Series (to be published in Summer of 2019)


We have decided to upload all the chapters of our book as soon as we finish editing them. We hope this might be useful to some of you who wish to learn more about the automorphic representations and trace formulae. Note that not all of the chapters have been linked. If you find typos or errors, please email me at

Available/Edited up to Chapter 16:

Chapter 1: Algebraic Groups
Chapter 2: Adeles
Chapter 3: Automorphic Representations
Chapter 4: Archimedean Representation Theory
Chapter 5: Representations of Totally Disconnected Groups
Chapter 6: Automorphic Forms
Chapter 7: Unramified Representations
Chapter 8: Nonarchimedean Representation Theory
Chapter 9: The Cuspidal Spectrum
Chapter 10: Eisenstein Series
Chapter 11: Rankin-Selberg L-functions
Chapter 12: Langlands Functoriality
Chapter 13: Known Cases of Global Langlands Functoriality
Chapter 14: Distinction and Period Integrals
Chapter 15: The Cohomology of Locally Symmetric Spaces
Chapter 16: Spectral Sides of Trace Formulae
Chapter 17: Orbital Integrals
Chapter 18: Simple Trace Formulae
Chapter 19: Applications of Trace Formulae
Appendix A: The Iwasawa Decomposition
Appendix B: Poisson Summation

    Springer GTM Series