Zero correlation with lower-order terms for automorphic L-functions
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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].
2021 ◽
Vol 28
(4)
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Keyword(s):
2000 ◽
Vol 101
(5)
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pp. 3408-3421
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Keyword(s):