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Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2).

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Title: Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2).
Authors: Tsang, Kin Ming1 (AUTHOR) kmtsang@math.ubc.ca
Source: Journal of Number Theory. Apr2026, Vol. 281, p1-42. 42p.
Subjects: Automorphic forms
Abstract: We consider a variant of the strong multiplicity one theorem. Let π 1 and π 2 be two unitary cuspidal automorphic representations for GL (2) that are not twist-equivalent. We find a lower bound for the lower Dirichlet density of the set of places for which | a v (π 1) | > | a v (π 2) | , where a v (π i) is the trace of the Langlands conjugacy class of π i at v. One consequence of this result is an improvement on the existing bound on the lower Dirichlet density of the set of places for which | a v (π 1) | ≠ | a v (π 2) |. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2).
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  Data: <searchLink fieldCode="AR" term="%22Tsang%2C+Kin+Ming%22">Tsang, Kin Ming</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> kmtsang@math.ubc.ca</i>
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  Data: We consider a variant of the strong multiplicity one theorem. Let π 1 and π 2 be two unitary cuspidal automorphic representations for GL (2) that are not twist-equivalent. We find a lower bound for the lower Dirichlet density of the set of places for which | a v (π 1) | > | a v (π 2) | , where a v (π i) is the trace of the Langlands conjugacy class of π i at v. One consequence of this result is an improvement on the existing bound on the lower Dirichlet density of the set of places for which | a v (π 1) | ≠ | a v (π 2) |. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jnt.2025.09.012
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      – Code: eng
        Text: English
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        PageCount: 42
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      – SubjectFull: Automorphic forms
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      – TitleFull: Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2).
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              Text: Apr2026
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