Journal article
Zero correlation with lower-order terms for automorphic L-functions
International journal of number theory, Vol.12(1), pp.27-55
02/2016
DOI: 10.1142/S1793042116500032
Abstract
Let [Formula: see text] be a self-contragredient automorphic cuspidal representation of [Formula: see text] for [Formula: see text]. Using a refined version of the Selberg orthogonality, we recompute the [Formula: see text]-level correlation of high non-trivial zeros of the product [Formula: see text]. In the process, we are able to extract certain low-order terms which suggest the asymptotics of these statistics are not necessarily universal, but depend upon the conductors of the representations and hence the ramification properties of the local components coming from each [Formula: see text]. The computation of these lower-order terms is unconditional as long as all [Formula: see text].
Details
- Title: Subtitle
- Zero correlation with lower-order terms for automorphic L-functions
- Creators
- Timothy L Gillespie - Department of Mathematics, St. Ambrose University, 518 West Locust Street, Davenport, IA 52803, USAYangbo Ye - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- International journal of number theory, Vol.12(1), pp.27-55
- DOI
- 10.1142/S1793042116500032
- ISSN
- 1793-0421
- eISSN
- 1793-7310
- Language
- English
- Date published
- 02/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9983985847002771
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