Rank-two Euler systems for symmetric squares

Büyükboduk, Kâzım; Lei, Antonio

doi:10.1090/tran/7860

Rank-two Euler systems for symmetric squares
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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 $p$.

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