Journal article
Selberg's orthogonality conjecture for automorphic L-functions
American journal of mathematics, Vol.127(4), pp.837-849
2005
DOI: 10.1353/ajm.2005.0029
Abstract
Let π and π′ be automorphic irreducible unitary cuspidal representations of GLm(ℚdouble-struck A sign) and GLm′(ℚdouble-struck A sign), respectively. Assume that either π or π′ is self contragredient. Under the Ramanujan conjecture on π and π′, we deduce a prime number theorem for L(s, π × π̃′), which can be used to asymptotically describe whether π′ ≅ π, or π′ ≅ π ⊗ | det(·)|iτ0 for some nonzero τ0 ε ℝ, or π′ ≇ π ⊗ | det(·)|it for any t ε ℝ. As a consequence, we prove the Selberg orthogonality conjecture, in a more precise form, for automorphic L-functions L(s, π) and L(s, π′), under the Ramanujan conjecture. When m = m′ = 2 and π and π′ are representations corresponding to holomorphic cusp forms, our results are unconditional.
Details
- Title: Subtitle
- Selberg's orthogonality conjecture for automorphic L-functions
- Creators
- Jianya LiuYangbo Ye
- Resource Type
- Journal article
- Publication Details
- American journal of mathematics, Vol.127(4), pp.837-849
- Publisher
- Johns Hopkins University Press
- DOI
- 10.1353/ajm.2005.0029
- ISSN
- 0002-9327
- eISSN
- 1080-6377
- Language
- English
- Date published
- 2005
- Academic Unit
- Mathematics
- Record Identifier
- 9984241149202771
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