Factoring 𝐿-functions as products of 𝐿-functions

Grenier, Douglas

doi:10.1090/S0002-9947-1994-1273533-8

Factoring $L$-functions as products of $L$-functions
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by Douglas Grenier

Trans. Amer. Math. Soc. 345 (1994), 673-692

DOI: https://doi.org/10.1090/S0002-9947-1994-1273533-8

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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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