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The
nonvanishing of the trace of $T_3$
Liubomir Chiriac, Daphne Kurzenhauser and Erin Williams |
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Vol. 17 (2024), No. 2, 263–272
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Abstract |
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A generalized Lehmer conjecture predicts that, for every positive integer , the trace of the Hecke operator in level 1 does not vanish, unless the space of cusp forms acted upon is trivial. So far, this has only been established for . We use -adic methods to prove the statement for . |
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Keywords
modular forms, Hecke operators, trace formula
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Mathematical Subject Classification
Primary: 11F30
Secondary: 11B37, 11F85
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Milestones
Received: 28 June 2022
Revised: 15 September 2022
Accepted: 7 February 2023
Published: 20 May 2024
Communicated by Kenneth S. Berenhaut
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Authors |
| Liubomir Chiriac | |
| Fariborz Maseeh Department of
Mathematics and Statistics Portland State University Portland, OR United States |
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| Daphne Kurzenhauser | |
| Fariborz Maseeh Department of
Mathematics and Statistics Portland State University Portland, OR United States |
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| Erin Williams | |
| Fariborz Maseeh Department of
Mathematics and Statistics Portland State University Portland, OR United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
