Journal article
A proof of Selberg's orthogonality for automorphic L-functions
manuscripta mathematica, Vol.118(2), pp.135-149
10/2005
DOI: 10.1007/s00229-005-0563-4
Abstract
Let π and π′ be automorphic irreducible cuspidal representations of GLm(QA) and GLm′(QA), respectively. Assume that π and π′ are unitary and at least one of them is self-contragredient. In this article we will give an unconditional proof of an orthogonality for π and π′, weighted by the von Mangoldt function Λ(n) and 1−n/x. We then remove the weighting factor 1−n/x and prove the Selberg orthogonality conjecture for automorphic L-functions L(s,π) and L(s,π′), unconditionally for m≤4 and m′≤4, and under the Hypothesis H of Rudnick and Sarnak [20] in other cases. This proof of Selberg's orthogonality removes such an assumption in the computation of superposition distribution of normalized nontrivial zeros of distinct automorphic L-functions by Liu and Ye [12].
Details
- Title: Subtitle
- A proof of Selberg's orthogonality for automorphic L-functions
- Creators
- Jianya Liu - Department of Mathematics Shandong University JinanShandong250100ChinaYonghui Wang - Department of Mathematics Capital Normal University Beijing100037ChinaYangbo Ye - Department of Mathematics The University of Iowa Iowa CityIowa52242-1419USA
- Resource Type
- Journal article
- Publication Details
- manuscripta mathematica, Vol.118(2), pp.135-149
- DOI
- 10.1007/s00229-005-0563-4
- ISSN
- 0025-2611
- eISSN
- 1432-1785
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- Language
- English
- Date published
- 10/2005
- Academic Unit
- Mathematics
- Record Identifier
- 9983985996002771
Metrics
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