This book focuses on a conjectural class of zeta integrals which arose from a program born in
the work of Braverman and Kazhdan around the year 2000 the eventual goal being to prove the
analytic continuation and functional equation of automorphic L-functions. Developing a general
framework that could accommodate Schwartz spaces and the corresponding zeta integrals the
author establishes a formalism states desiderata and conjectures draws implications from
these assumptions and shows how known examples fit into this framework supporting
Sakellaridis' vision of the subject. The collected results both old and new and the included
extensive bibliography will be valuable to anyone who wishes to understand this program and
to those who are already working on it and want to overcome certain frequently occurring
technical difficulties.
