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

[2408.01643] Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2) Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:2408.01643 (math) [Submitted on 3 Aug 2024 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2) Authors: Kin Ming Tsang View a PDF of the paper titled Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2), by Kin Ming Tsang View PDF HTML (experimental) Abstract: We consider a variant of the strong multiplicity one theorem. Let $\pi_{1}$ and $\pi_{2}$ be two unitary cuspidal automorphic representations for $\mathrm{GL(2)}$ that are not twist-equivalent. We find a lower bound for the lower Dirichlet density of the set of places for which $\left\lvert a_{v}(\pi_{1}) \right\rvert > \left\lvert a_{v}(\pi_{2}) \right\rvert$, where $a_{v}(\pi_{i})$ is the trace of Langlands conjugacy class of $\pi_{i}$ 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 $\left\lvert a_{v}(\pi_{1})\right\rvert \neq \left\lvert a_{v}(\pi_{2}) \right\rvert$. Comments: Revised version Subjects: Number Theory (math.NT) MSC classes: 11F30 (Primary), 11F41 (Secondary) Cite as: arXiv:2408.01643 [math.NT] (or arXiv:2408.01643v3 [math.NT] for this version) https://doi.org/10.48550/arXiv.2408.01643 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Number Theory 281 (2026) Related DOI : https://doi.org/10.1016/j.jnt.2025.09.012 Focus to learn more DOI(s) linking to related resources Submission history From: Kin Ming Tsang [ view email ] [v1] Sat, 3 Aug 2024 03:00:52 UTC (20 KB) [v2] Wed, 16 Apr 2025 19:26:33 UTC (23 KB) [v3] Tue, 14 Apr 2026 19:34:26 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Comparing Hecke eigenvalues for pairs of automorphic representations for GL(2), by Kin Ming Tsang View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2024-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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