Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300787110> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W4300787110 abstract "Iwasawa theory of modular forms over anticyclotomic $mathbb{Z}_p$-extensions of imaginary quadratic fields has been studied by several authors, starting from the works of Bertolini-Darmon and Iovita-Spiess, under the crucial assumption that the prime $p$ is unramified in $K$. We start in this article the systematic study of anticyclotomic $p$-adic $L$-functions when $p$ is ramified in $K$. In particular, when $f$ is a weight $2$ modular form attached to an elliptic curve $E/mathbb{Q}$ having multiplicative reduction at $p$, and $p$ is ramified in $K$, we show an analogue of the exceptional zeroes phenomenon investigated by Bertolini-Darmon in the setting when $p$ is inert in $K$. More precisely, we consider situations in which the $p$-adic $L$-function $L_p(E/K)$ of $E$ over the anticyclotomic $mathbb{Z}_p$-extension of $K$ does not vanish identically but, by sign reasons, has a zero at certain characters $chi$ of the Hilbert class field of $K$. In this case we show that the value at $chi$ of the first derivative of $L_p(E/K)$ is equal to the formal group logarithm of the specialization at $p$ of a global point on the elliptic curve (actually, this global point is a twisted sum of Heegner points). This generalizes similar results of Bertolini-Darmon, available when $p$ is inert in $K$ and $chi$ is the trivial character." @default.
- W4300787110 created "2022-10-04" @default.
- W4300787110 creator A5011581244 @default.
- W4300787110 creator A5042269572 @default.
- W4300787110 date "2017-07-19" @default.
- W4300787110 modified "2023-10-16" @default.
- W4300787110 title "Exceptional zero formulae for anticyclotomic p-adic L-functions of elliptic curves in the ramified case" @default.
- W4300787110 doi "https://doi.org/10.48550/arxiv.1707.06019" @default.
- W4300787110 hasPublicationYear "2017" @default.
- W4300787110 type Work @default.
- W4300787110 citedByCount "0" @default.
- W4300787110 crossrefType "posted-content" @default.
- W4300787110 hasAuthorship W4300787110A5011581244 @default.
- W4300787110 hasAuthorship W4300787110A5042269572 @default.
- W4300787110 hasBestOaLocation W43007871101 @default.
- W4300787110 hasConcept C105795698 @default.
- W4300787110 hasConcept C114614502 @default.
- W4300787110 hasConcept C118615104 @default.
- W4300787110 hasConcept C129844170 @default.
- W4300787110 hasConcept C134306372 @default.
- W4300787110 hasConcept C138885662 @default.
- W4300787110 hasConcept C139676723 @default.
- W4300787110 hasConcept C166437778 @default.
- W4300787110 hasConcept C179603306 @default.
- W4300787110 hasConcept C202444582 @default.
- W4300787110 hasConcept C2524010 @default.
- W4300787110 hasConcept C2780813799 @default.
- W4300787110 hasConcept C2781089630 @default.
- W4300787110 hasConcept C33923547 @default.
- W4300787110 hasConcept C39927690 @default.
- W4300787110 hasConcept C41895202 @default.
- W4300787110 hasConcept C75764964 @default.
- W4300787110 hasConcept C94375191 @default.
- W4300787110 hasConcept C95136341 @default.
- W4300787110 hasConceptScore W4300787110C105795698 @default.
- W4300787110 hasConceptScore W4300787110C114614502 @default.
- W4300787110 hasConceptScore W4300787110C118615104 @default.
- W4300787110 hasConceptScore W4300787110C129844170 @default.
- W4300787110 hasConceptScore W4300787110C134306372 @default.
- W4300787110 hasConceptScore W4300787110C138885662 @default.
- W4300787110 hasConceptScore W4300787110C139676723 @default.
- W4300787110 hasConceptScore W4300787110C166437778 @default.
- W4300787110 hasConceptScore W4300787110C179603306 @default.
- W4300787110 hasConceptScore W4300787110C202444582 @default.
- W4300787110 hasConceptScore W4300787110C2524010 @default.
- W4300787110 hasConceptScore W4300787110C2780813799 @default.
- W4300787110 hasConceptScore W4300787110C2781089630 @default.
- W4300787110 hasConceptScore W4300787110C33923547 @default.
- W4300787110 hasConceptScore W4300787110C39927690 @default.
- W4300787110 hasConceptScore W4300787110C41895202 @default.
- W4300787110 hasConceptScore W4300787110C75764964 @default.
- W4300787110 hasConceptScore W4300787110C94375191 @default.
- W4300787110 hasConceptScore W4300787110C95136341 @default.
- W4300787110 hasLocation W43007871101 @default.
- W4300787110 hasOpenAccess W4300787110 @default.
- W4300787110 hasPrimaryLocation W43007871101 @default.
- W4300787110 hasRelatedWork W2046049376 @default.
- W4300787110 hasRelatedWork W2075819216 @default.
- W4300787110 hasRelatedWork W2114942681 @default.
- W4300787110 hasRelatedWork W2138854794 @default.
- W4300787110 hasRelatedWork W2636899518 @default.
- W4300787110 hasRelatedWork W2951636250 @default.
- W4300787110 hasRelatedWork W2952252232 @default.
- W4300787110 hasRelatedWork W2963632765 @default.
- W4300787110 hasRelatedWork W3101202389 @default.
- W4300787110 hasRelatedWork W4299841628 @default.
- W4300787110 isParatext "false" @default.
- W4300787110 isRetracted "false" @default.
- W4300787110 workType "article" @default.