Big Heegner points and special values of L-series

Francesc Castella; Matteo Longo

doi:10.1007/s40316-015-0045-3

Big Heegner points and special values of L-series

Francesc Castella, Matteo Longo

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In Longo and Vigni (Manuscr Math 135:273–328, 2011), Howard’s construction of big Heegner points on modular curves was extended to general Shimura curves over the rationals. In this paper, we relate the higher weight specializations of the big Heegner points of Longo and Vigni (Manuscr Math 135:273–328, 2011) in the definite setting to certain higher weight analogues of the Bertolini–Darmon theta elements (Bertolini and Darmon in Invent Math 126:413–456, 1996). As a consequence of this relation, some of the conjectures in Longo and Vigni (Manuscr Math 135:273–328, 2011) are deduced from recent results of Chida and Hsieh (J Reine Angew Math, 2015).

Original language	English (US)
Pages (from-to)	303-324
Number of pages	22
Journal	Annales Mathematiques du Quebec
Volume	40
Issue number	2
DOIs	https://doi.org/10.1007/s40316-015-0045-3
State	Published - Aug 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Hida families
Modular forms
P-adic L-functions

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10.1007/s40316-015-0045-3

Cite this

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abstract = "In Longo and Vigni (Manuscr Math 135:273–328, 2011), Howard{\textquoteright}s construction of big Heegner points on modular curves was extended to general Shimura curves over the rationals. In this paper, we relate the higher weight specializations of the big Heegner points of Longo and Vigni (Manuscr Math 135:273–328, 2011) in the definite setting to certain higher weight analogues of the Bertolini–Darmon theta elements (Bertolini and Darmon in Invent Math 126:413–456, 1996). As a consequence of this relation, some of the conjectures in Longo and Vigni (Manuscr Math 135:273–328, 2011) are deduced from recent results of Chida and Hsieh (J Reine Angew Math, 2015).",

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Big Heegner points and special values of L-series

Abstract

All Science Journal Classification (ASJC) codes

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