Rank-two Euler systems for symmetric squares
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- by Kâzım Büyükboduk and Antonio Lei PDF
- Trans. Amer. Math. Soc. 372 (2019), 8605-8619 Request permission
Abstract:
Let $p\ge 7$ be a prime number, and let $f$ be a normalized eigen-newform with good reduction at $p$ such that its $p$th Fourier coefficient vanishes. We construct a rank-two Euler system attached to the $p$-adic realization of the symmetric square motive of $f$. Furthermore, we show that the nontriviality is guaranteed by the nonvanishing of the leading term of the relevant $L$-value and the nonvanishing of a certain $p$-adic period modulo $p$.References
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Additional Information
- Kâzım Büyükboduk
- Affiliation: UCD School of Mathematics and Statistics, University College Dublin, Dublin, Ireland
- Email: kazim.buyukboduk@ucd.ie
- Antonio Lei
- Affiliation: Département de Mathématiques et de Statistique, Université Laval, Pavillion Alexandre-Vachon, 1045 Avenue de la Médecine, Québec, Québec G1V 0A6, Canada
- MR Author ID: 902727
- ORCID: 0000-0001-9453-3112
- Email: antonio.lei@mat.ulaval.ca
- Received by editor(s): November 12, 2018
- Received by editor(s) in revised form: February 1, 2019, and March 27, 2019
- Published electronically: June 25, 2019
- Additional Notes: The first author received funding from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant Agreement No. 745691 (CriticalGZ)
The second author was supported by the NSERC Discovery Grants Program 05710. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 8605-8619
- MSC (2010): Primary 11R23; Secondary 11F11, 11R20
- DOI: https://doi.org/10.1090/tran/7860
- MathSciNet review: 4029706