Quadratic modular symbols on Shimura curves

Bayer, Pilar; Blanco-Chacón, Iván

doi:10.5802/jtnb.835

Bayer, Pilar ¹; Blanco-Chacón, Iván ²

¹ Facultat de Matemàtiques Universitat de Barcelona Gran Via de les Corts Catalanes, 585 08007 Barcelona, Spain
² Department of Mathematics and Systems Analysis Aalto University Otakaari 1, M FI-00076 Espoo, Finland

Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 261-283.

Abstract
Résumé

We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic $p$ -adic $L$ -functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic $p$ -adic $L$ -functions to more general Shimura curves.

Nous introduisons le concept de symbole modulaire quadratique et nous étudions comment ces symboles sont liés aux fonctions $L$ $p$ -adiques quadratiques. Ces objets ont été introduits dans [3] dans le cas des courbes modulaires. Dans cet article, nous proposons une méthode pour attacher des symboles modulaires et fonctions $L$ $p$ -adiques quadratiques aux courbes de Shimura plus générales.

MR Zbl

DOI: 10.5802/jtnb.835

Author's affiliations:

Bayer, Pilar ¹; Blanco-Chacón, Iván ²

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     author = {Bayer, Pilar and Blanco-Chac\'on, Iv\'an},
     title = {Quadratic modular symbols on {Shimura} curves},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {261--283},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {2},
     year = {2013},
     doi = {10.5802/jtnb.835},
     zbl = {1295.11052},
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Bayer, Pilar; Blanco-Chacón, Iván. Quadratic modular symbols on Shimura curves. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 2, pp. 261-283. doi : 10.5802/jtnb.835. http://archive.numdam.org/articles/10.5802/jtnb.835/

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