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- W4295888026 abstract "Let $q$ be any prime $equiv 7 mod 16$, $K = mathbb{Q}(sqrt{-q})$, and let $H$ be the Hilbert class field of $K$. Let $A/H$ be the Gross elliptic curve defined over $H$ with complex multiplication by the ring of integers of $K$. We prove the existence of a large explicit infinite family of quadratic twists of $A$ whose complex $L$-series does not vanish at $s=1$. This non-vanishing theorem is completely new when $q > 7$. Its proof depends crucially on the results established in our earlier paper for the Iwasawa theory at the prime $p=2$ of the abelian variety $B/K$, which is the restriction of scalars from $H$ to $K$ of the elliptic curve $A$." @default.
- W4295888026 created "2022-09-16" @default.
- W4295888026 creator A5010299935 @default.
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- W4295888026 date "2019-04-11" @default.
- W4295888026 modified "2023-10-18" @default.
- W4295888026 title "Non-vanishing theorems for central $L$-values of some elliptic curves with complex multiplication II" @default.
- W4295888026 doi "https://doi.org/10.48550/arxiv.1904.05756" @default.
- W4295888026 hasPublicationYear "2019" @default.
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