The amplification method in the GL(3) Hecke algebra
Roman Holowinsky, Guillaume Ricotta, Emmanuel Royer
TL;DR
This paper develops the technical tools necessary to construct an explicit and unconditional amplifier for GL(3) automorphic forms, including detailed coset decomposition computations in the Hecke algebra.
Contribution
It provides the first comprehensive implementation framework for an explicit amplifier in the GL(3) setting, with detailed algebraic computations.
Findings
Explicit coset decompositions in GL(3) Hecke algebra
Framework for effective automorphic form amplification
Unconditional amplifier construction methods
Abstract
This article contains all of the technical ingredients required to implement an effective, explicit and unconditional amplifier in the context of GL(3) automorphic forms. In particular, several coset decomposition computations in the GL(3) Hecke algebra are explicitly done.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Analytic Number Theory Research · Algebraic Geometry and Number Theory