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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Factoring $ L$-functions as products of $ L$-functions


Author: Douglas Grenier
Journal: Trans. Amer. Math. Soc. 345 (1994), 673-692
MSC: Primary 11F60; Secondary 11F66, 11F70
MathSciNet review: 1273533
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Abstract: We will demonstrate two factorizations of L-functions associated with automorphic forms on $ GL(n,\mathbb{R})$, where one factor is a Riemann zetafunction and the other is an L-function associated to an automorphic form for $ GL(n - 1,\mathbb{R})$. These will be obtained by establishing the commutation of the Hecke operators and the $ \Phi $-operator, a homomorphism from automorphic forms on $ GL(n,\mathbb{R})$ to automorphic forms on $ GL(n - 1,\mathbb{R})$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1273533-8
PII: S 0002-9947(1994)1273533-8
Article copyright: © Copyright 1994 American Mathematical Society