Rank-two Euler systems for symmetric squares

Rank-two Euler systems for symmetric squares

Let p\ge 7 be a prime number, and let f be a normalized eigen-newform with good reduction at p such that its pth 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 g...

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Veröffentlicht in:Transactions of the American Mathematical Society 2019-12, Vol.372 (12), p.8605-8619
Hauptverfasser: Büyükboduk, Kâzım, Lei, Antonio
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description Let p\ge 7 be a prime number, and let f be a normalized eigen-newform with good reduction at p such that its pth 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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