EXCEPTIONAL ZEROES OF P-ADIC L-FUNCTIONS OVER NON-ABELIAN FIELD EXTENSIONS
2015 ◽
Vol 58
(2)
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pp. 385-432
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AbstractSuppose E is an elliptic curve over $\Bbb Q$, and p>3 is a split multiplicative prime for E. Let q ≠ p be an auxiliary prime, and fix an integer m coprime to pq. We prove the generalised Mazur–Tate–Teitelbaum conjecture for E at the prime p, over number fields $K\subset \Bbb Q\big(\mu_{{q^{\infty}}},\;\!^{q^{\infty}\!\!\!\!}\sqrt{m}\big)$ such that p remains inert in $K\cap\Bbb Q(\mu_{{q^{\infty}}})^+$. The proof makes use of an improved p-adic L-function, which can be associated to the Rankin convolution of two Hilbert modular forms of unequal parallel weight.
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2013 ◽
Vol 37
(1)
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pp. 1-11
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2011 ◽
Vol 147
(3)
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pp. 716-734
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2012 ◽
Vol 153
(3)
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pp. 471-487
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Keyword(s):
1987 ◽
Vol 55
(4)
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pp. 765-838
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