Abstract
Zeta integrals are indispensable tools for studying automorphic representations and their L-functions. In broad terms, it involves integrating automorphic forms (global case) or “coefficients” of representations (local case) against suitable test functions such as Eisenstein series or Schwartz–Bruhat functions; furthermore, these integrals are often required to have meromorphic continuation in some complex parameter λ and satisfy certain symmetries, i.e. functional equations. These ingenious constructions are usually crafted on a case-by-case basis; systematic theories are rarely pursued with a notable exception (Sakellaridis, Algebra Number Theory 6:611–667, 2012), which treats only the global zeta integrals. The goal of this work is to explore some aspects of this general approach, with an emphasis on the local formalism.
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Li, WW. (2018). Introduction. In: Zeta Integrals, Schwartz Spaces and Local Functional Equations. Lecture Notes in Mathematics, vol 2228. Springer, Cham. https://doi.org/10.1007/978-3-030-01288-5_1
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